FOREST MENSURATION
C. A. SCHENCK, Ph.D.
Director Biltmore Forest School, and Fort
the Biltmore Estate
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FOREST MENSURATION
By
C. A. SCHENCK, Ph.D.
Director Biltmore Forest School, and Forester to
the Biltmore Estate
MCMV
THE UNIVERSITY PRESS
of SEWANEE TENNESSEE
Digitized by the Internet Archive
in 2009 with funding from
NCSU Libraries
http://www.archive.org/details/forestmensuratioOOsche
PREFACE
Dear Readers :
In the following pages an attempt is made to treat "Forest Men
suration" from a scientificmathematical standpoint as well as from
the view point of practical application.
Naturally, pamphlets of as restricted a character as this treatise on
forest mensuration address themselves to a very restricted circle of
readers ; and the expense of printing is never covered by the returns from
sales.
Thus it becomes necessary, in order to reduce the expense of pub
lication, to omit all, or practically all, lengthy explanation of a mathe
matical nature which the teacher at a forest school can easily supply
in the course of his lectures.
The present Biltmore pamphlet on Forest Mensuration is intended,
above all, to assist the students enlisted at the Biltmore School. It con
tains the teacher's dictation which the students, in former years, were
compelled to take down in long or shorthand, to the annoyance of both
teacher and students.
It cannot be expected that a presentday lumberman will take a direct
and personal interest in any of the following paragraphs. Still, in con
servative forestry, in destructive forestry, and in any other business en
terprise, the truism is worth remembering that "knowledge is the best
of assets."
Knowledge certainly forms the only unalienable factor of production.
With the advent of high stumpage prices, the owner of woodland will
be inclined to consider, under many circumstances, the advisability of
foresthusbandry — an idea which was as preposterous in past decades of
superabundance of timber as the raising of beef cattle, some sixty years
ago, in the prairies then abounding in buffalo.
Financially considered, a proper outcome of foresthusbandry is and
must be based on a proper application of the theories and principles
involved in forest mensuration.
I shall be deeply grateful to a kind reader who, discovering mistakes
or incongruities in the following paragraphs, will take the trouble of
sending me a timely hint. Most truly,
C. A. SCHENCK,
Director Biltmore Forest School, and
Forester to the Biltmore Estate.
August i, 1905.
LECTURES ON FOREST MENSURATION
SYNOPSIS OF CONTENTS BY PARAGRAPHS.
Par.
I. Definition and subdivision.
Par.
II.
Par.
III.
Par.
IV.
Par.
V.
Par.
VI.
Par.
VII.
Par.
VIII.
Par
IX.
Par.
X.
Par.
XI.
Par.
XII.
Par.
XIII.
Par.
XIV.
Par.
XV.
Par.
XVI.
Par.
XVII.
Par.
XVIII.
Par.
XIX
Par.
XX.
Par.
XXI.
Par.
XXII.
Par.
XXIII.
Par.
XXIV.
Par.
XXV.
Par.
Si
XXVI.
Par.
XXVII.
Par.
XXVIII.
Par.
XXIX.
Par.
XXX.
Par.
XXXI.
Par.
XXXII.
Par.
XXXIII.
Par.
XXXIV.
CHAPTER I.— VOLUME.
Section I.— Volume of Trees Cut Down.
Units of volume.
Mathematical form of trees.
Cylinder
Apollonian Paraboloid.
Cone.
Ne ill's paraboloid.
Riecke's, Huber's and Smalian's formule.
Hossfeld's formule.
Simony's formule.
Sectional measurement.
Measuring the length of a log.
Measuring the sectional area.
Instruments for measuring diameters.
Units of log measurement in the United States.
Boardrules.
Standardrules.
Cubic footrules.
Equivalents.
Xylometric method.
Hydrostatic method.
Factors influencing the solid contents of cordwood.
Reducing factors for cordwood.
Local peculiarities with reference to stacked wood.
Bark.
Section II. — Volume oe Standing Trees.
Methods of obtaining the volume of standing trees.
Helps and hints to find the volume of standing trees.
Scientific methods of ascertaining the cubic contents of
standing trees by mere measurement.
Form factor method.
Kinds of form factors mathematically.
Kinds of common form factors in European practice.
Means for exact mensuration of standing trees.
Measuring the height of a standing tree.
Factors influencing the exactness of hypsometrical ob
servations.
VI.
Forest Mensuration
Par.
XXXV.
Par.
XXXVI.
Par.
XXXVII.
Par.
XXXVIII
Indirect mensuration of diameter.
Pressler's telescope.
Auxiliaries for calculation.
Tree volume tables.
Par.
XXXIX.
Par.
XL.
Par.
XLI.
Par.
XLII.
Par.
XLIII.
Par.
XLIV.
Par.
XXV.
Par
XL VI.
Par.
XLVII.
Par.
XLVIII.
Par.
XLIX,
Par.
L.
Par
LI.
Par.
LII.
Par.
LIU.
Par.
LIV.
Par.
LV.
Par.
LVI.
Par.
LVII.
Par.
LVIII.
Par.
LIX.
Par.
LX.
Par.
LXI.
Par.
LXII.
Par.
LXIII.
Par.
LXIV.
Par.
LXV.
Par.
LXVI.
Par.
LXVII.
Par.
LXVIII.
Section III. — Volume of Forests.
Synopsis of methods for ascertaining the volume of
forests.
Estimation of forest volume.
Principles underlying the exact mensuration of forest
volume.
Field work for exact valuation surveys.
Basal assumptions.
Selection of sample trees.
DraudtUrich method.
Robert Hartig method.
Average sampletree method.
Exact mensuration without cutting sample trees.
Combined measuring and estimating.
Form factor method.
Form height method.
Volume table method.
Yield table method.
Distance figure.
Algon's Universal Volume Tables.
Schenck's graphic method.
Factors governing the selection of a method of valuation
survey
Factors influencing the selection of sample plots.
Sir D. Brandis method.
PinchotGraves method on Webb estate.
The gridironing method.
Forest reserve methods.
Sample squares.
Pisgah Forest method of 1896.
Pisgah Forest method for stumpage sale, bark sale and
lumbering operations.
Henry Gannett's method, adopted for the XHth census.
A forty method used in Michigan.
Dr. Fernow's forty method used at Axton.
CHAPTER II— AGE OF TREES AND OF FORESTS.
Par. LXIX. Age of trees cut down.
Par. LXX. Age of standing trees.
Par. LXXI. Age of a forest.
Forest Mensuration
vn.
Par.
CHAPTER III.— INCREMENT OF TREES AND OF FORESTS.
Section I. — Increment of a Tree.
The kinds of increment.
Height increment.
The current height increment.
The average height increment.
Relative increment of the height.
Diameter increment.
Sectional area increment.
Relative increment of diameter and of sectional area.
Volume increment.
Section analysis.
Noerdlinger's paperweight method.
Schenck's graphic tree analysis.
Wagener's method and stump analysis.
Pressler's method.
Breyman's method.
Factors influencing the cubic volume increment.
Volume increment percentage of standing trees.
Interdependence between cubic increment and increment
in feet b. m., Doyle.
Construction of volume tables.
Par.
LXXII.
Par.
LXXIII.
Par.
LXXIV.
Par.
LXXV.
Par.
LXXVI.
Par.
LXXVII.
Par.
LXXVIII.
Par.
LXXIX.
Par.
LXXX.
Par.
LXXXI.
Par.
LXXXII
Par
LXXXIII.
Par.
LXXXIV.
Par.
LXXXV.
Par.
LXXXVI.
Par.
LXXXVII.
Par.
LXXXVIII.
Par.
LXXXIX.
xc.
Par.
XCI.
Par.
XCII.
Par.
XCIII.
Par.
XCIV.
Par.
xcv.
Par.
XCVI.
Par.
XCVII.
Par.
XCVIII.
Par.
XCIX.
Section II. — Increment of a Wood.
Increment of forests.
Method of construction of normal yield tables.
Gathering data for normal yield tables.
Normal yield tables, their purpose and contents abroad.
Retrospective yield tables.
Yield tables of the Bureau of Forestry.
The increment of a woodlot.
Ascertaining the increment of woodlots by sample trees.
Current increment ascertained from average increment.
Par.
Par.
CHAPTER IV.— LUMBER.
C. Units of lumber measure.
CI. Inspection rules and nomenclature.
Par.
CHAPTER V.— STUMPAGEVALUES.
CII. Stumnaaievalues.
FOREST MENSURATION
PARAGRAPH I.
DEFINITION AND SUBDIVISION.
Definition : By "Forest Mensuration," the forester ascertains the vol
ume, the age, the increment and the stumpage value of trees, parts of
trees and aggregates of trees. As a branch of forestry, forest mensura
tion may be divided into the following five parts :
I. Determination of volume of trees cut down, of standing trees
and of forests.
II. Determination of age of trees and of forests.
III. Determination of increment of trees and of forests.
IV. Determination of sawn lumber.
V. Determination of stumpage value.
Circular 445 of the Bureau of Forestry defines mensuration as "the
determination of the present and future product of the forest."
American literature is found in Bulletin 20, Division of Forestry; Bul
letin 36, Bureau of Forestry ; S. B. Green, page 132 ; Lumber & Log Book
and Lumberman's Handbook, edited by the "American Lumberman."
CHAPTER I.— VOLUME.
SECTION I.— VOLUME OF TREES CUT DOWN.
PARAGRAPH II.
UNITS OF VOLUME.
The volume of a tree or of a tree section is expressed :
1. For scientific purposes, on the basis of exact measurements, in
cubic feet or cubic meters.
2. For practical purposes, by estimates according to local usage, often
assisted by partial measurement, in local units (feet board
measure; standards; cords; cubic feet; cord feet; etc.).
PARAGRAPH III.
MATHEMATICAL FORM OF TREES.
Trees do not grow, like crystals, according to purely mathematical laws.
Tree growth is deeply influenced by individuality, by surroundings, by
accidental occurrences, etc.
2
2 Forest Menstiration
The body of a tree, considered as a conoid (a solid body formed by
the revolution of a curve about an axis), is very complicated, being
formed by a curve of high power. This is the case even in straight and
clear boled conifers. The tree bole shows, however, in certain sections
of its body frequently a close resemblance to a truncated neilloid, cylinder,
paraboloid and cone.
The longitudinal section of conoids is outlined by a curve correspond
ing with the general equation
y 2 = px«
in which y is the ordinate (corresponding with the radius of the basal
area), x the abscissa (representing the height of the conoid), n the
power of the curve ; whilst p is merely a constant factor. The volume
v of the conoid is obtained by integral calculus :
v _ y 2 7tx
n + 1
It is equal to sectional area, s, times height, h, over (nji).
The truncated volumes are developed by deducting a small top conoid
from a large total conoid.
Stht — s 2 h 2
vol. tronc.=
n + 1
In the general curve equation
y 2 = px«
we find represented :
A. For n equal to o, the cylinder;
B. For n equal to i, the Apollonian paraboloid, wherein the ratio
between sectional area and height is constant ;
C. For n equal to 2, the cone, wherein the ratio between radius of
sectional area and height is constant;
D. For n equal to 3, Neill's paraboloid, the truncated form of which
is found at the basis of our trees.
The top of the tree resembles a cone or Neilloid ; the main bole
resembles the cylinder or the Apollonian paraboloid.
The cross section (see Par. XIII.) through a tree taken perpen
dicular to its axis shows a more or less circular form. Near
sets of branches and near the roots, however, the outline is
irregular. The center of the circle usually fails to coincide with
the axis of the tree.
PARAGRAPH IV.
CYLINDER.
The cubic contents v of a cylinder are equal to the height h of the
cylinder, multiplied by the sectional area J of the cylinder.
vol. cylinder = h.s
sux>\
Forest Mensuration
€ K
3
PARAGRAPH V.
APOLLONIAN PARABOLOID.
The volume v of the Apollonian paraboloid is equal to height multi ■
plied by Yi sectional area, or equal to ^ of a cylinder having the same
height and the same basal area.
h.s
vol. apol. =  —
The volume t of the truncated Apollonian paraboloid may be ascer
tained as :
A. Height of trunk times arithmetical mean of top sectional area
and base sectional area.
s t + s„
t. apol. = h
2
B. Height of trunk times sectional area in the midst of the trunk.
t. apol. = h.sj
PARAGRAPH VI.
CONE.
The volume of the ordinary cone is equal to height of cone times 1/3
sectional area at the base.
h.s
vol. coDe = —
3
The volume t of the truncated cone is equal to 1/3 height of trunk
times sum total of top sectional area si, basal sectional area S2, and V si S2
h t/
t. cone = — (Sj + s 2 + V s 1 s 2 )
PARAGRAPH VII.
NEILL's PARABOLOID.
The volume of the Neilloid equals Y\ of its height times sectional area
at the base.
vol. neil. =
h.s
The volume of the truncated neilloid t equals
t. neil. = — ( s t + s 2 + &&^* [^ s"7+ f s^] J
wherein h denotes the height of the trunk; Sj and s 2 the top sectional
area and the basal sectional area of the trunk.
\{H js\V
Forest *minsuration
X
PARAGRAPH VIII.
riecke's, huber's and smalian's formule.
J
* Formules of practical and scientific application, used here and abroad,
to ascertain the contents of logs, are those published by Smalian, Riecke
and Huber.
^M»^V Riecke's formula holds good for n equal to o, I and 2, and is almost
correct for the neilloid.
Smalian overestimates and Huber underestimates the actual contents
of the truncated cone and of the truncated neilloid.
h
Riecke — Vol. of trunk = — (Sj + 4s i + s 2)
6
Huber — Vol. of trunk = h.sj
h
Smalian — Vol. of trunk = — (s t f s 2 )
Si designates the sectional area in the midst of the trunk, whilst si and S2
represent basal sectional area and top sectional area.
PARAGRAPH IX.
hossfeld's formule.
The formule given by Hossfeld is :
h
Vol. of trunk = — (3 S + s 2 )
4
It holds good for cylinder, cone and paraboloid. Si designates* the sec
tional area at J of the height of the trunk.
PARAGRAPH X.
simony's formule.
Simony's formule requires measurements of sectional areas at J4, *A
and 24 of the height of the trunk, thus avoiding the irregularities caused
by the roots at the base and by the branches at the top of a treetrunk.
h
Vol. of trunk = — (2 S — sj f 2 S )
This formule holds good for the four standard conoids.
PARAGRAPH XL
SECTIONAL measurement.
The formules given in Paragraphs III. to X. have, in C. A. Schenck's
opinion, a historic interest only when applied to whole trees. It is much
safer to ascertain the volume of a tree bole by dissecting it into (imag
Forest Mensuration 5
inary) log sections of equal length, considering each of such sections
as a cylinder or as a truncated paraboloid. The shorter the length of
the sections, the greater the accuracy of the result. In scientific research,
the length of a section varies from 5 feet to 10 feet. Obviously, at the
top of the bole an uneven length is left, which it might be wise to ascer
tain as a cone (or paraboloid — Bulletin 20). The volume of the total
bole, from stump to tip, equals, if the length of such full section is "\,"
and that of the top cone is "b," and
1 ) if sectional areas si, S2, S3, s n are measured at the big end of each
section :
vol bole =(s 1 +2s 2 + 2s, + s n ) + ~
2) if sectional areas Si,Sn, Sm, s m are measured in the midst of each
full section, and sectional area s n at the basis of the top cone :
b.Sn
vol. bole = 1 (si f Sn f Sin + s m ) f
The former formula is based on Smalian and the latter on Huber.
In a similar way, and with still greater accuracy, the more complicated
formulas of Riecke, Hossfeld and Simony might be adapted to sectional
measurements.
Remark : If the diameter in the middle of a log is larger than the
arithmetical mean of the end diameters, then the log contains more vol
ume than the truncated cone, and vice versa.
If the sectional area at the midst of the log is larger than the arith
metical mean of the end sectional areas, then the log contains more
volume than the truncated paraboloid, and vice versa. *
PARAGRAPH XII.
MEASURING THE LENGTH OF A LOG.
The length of a log is measured with tape, stick or axe handle. In
American logging, logs are usually cut in lengths of even feet, increased
by an addition of two inches to six inches, which addition allows for
shrinkage, for season checks, for damage to the log ends inflicted by
snaking or driving, and for the trimming in the saw mill required to
removed such end defects.
In Continental Europe, the standard log lengths are multiples of even
decimeters. An excesslength of up to eight inches is neglected.
Crooked logs are made straight by deductions either from the length
or from the diameter. Crooked trees should be dissected into very shor*
logs.
The standard length of a New England log is 13 feet.
In the case of big logs, great care must be taken by the sawyers to
obtain endcuts perpendicular to the axis of the log.
The sum of the lengths of logs cut from a tree is termed "used length."
The total length of that portion of a bole which is merchantable under
given conditions is called "merchantable length."
^N**JsJL
^%> V % f «OA^*^
6 Forest Mensuration
PARAGRAPH XIII.
MEASURING THE SECTIONAL AREA.
The sectional areas are ascertained with the help of measuring tape,
caliper, tree shears, tree compasses, Biltmore measuring stick, etc.
The sectional area is thus derived from the measurement either of the
diameter or of the circumference.
For exact scientific investigations the planimeter or the weight of an
evensized piece of paper may be used.
It is best to consider the sectional area of a tree as an ellipse, the
surface of which is :
TV
surface = — D.d,
4
the big diameter D being measured vertically to the small diameter d.
Usually, however, the average diameter of the tree at a given point
is found as the arithmetical mean of the big and small diameter at that
point measured crosswise and not as the square root of the product of
such diameters. Since
D + d ,
the average diameter is invariably, though slightly, overestimated by
crosswise measurement. Hence it is wise to drop, as an arbitrary offset,
the excess of fractions of inches over full inches.
The arithmetical mean of the sectional areas belonging to diameters
measured crosswise leads to still greater mistakes.
»
PARAGRAPH XIV.
INSTRUMENTS FOR MEASURING DIAMETERS.
Log calipers are made of pyrus wood or of metal. American make
(Morley Bros., Saginaw, Mich.) cost $4.00 each. The moving leg of the
caliper is kept in place by a spring or a screw or a wedge.
The best European makes are the "Friedrich" and the "Heyer and
Staudinger." Wimmenauer's "additioncaliper". counts the trees and adds
their sectional areas automatically.
Short legged calipers, named "Dachshunds" by C. A. Schenck, can be
used for trees the radius of which exceeds the length of the legs. The
diameter is, in that case, indirectly found by the help of the secant joining
the tips of the legs, which are about 5" long.
"Tree compasses," opening from six inches to thirtysix inches, and
made of nickelplated steel, cost (at Morley Bros.) $7.50. "Tree shears"
(Treffurth) find the angle formed by the shearlegs when pressed against
the tree and directly derive therefrom the diameter or the sectional area
of the tree.
The "diameter tape" slung around the tree usually yields too large a
diameter, since the circle embraces the maximum of surface by the min
imum of length.
Forest Mensuration
The "Biltmore Measuring Stick" can be well used in timber cruising.
It requires the exact adjustment of distance between eye and fist of ob
server (usually 26 inches), and gives directly the diameter at the point
of the stick where the sight line passes the tree tangentially. The stick
is held horizontally against the tree.
26inch Biltmore Measuring Stick.
Length on
the stick.
Diameter
with bark.
Contents of
butt log.
Contents of
two logs.
Contents of
three logs.
2.8"
54"
77"
9.9"
3"
6"
9"
12"
Allowing three inches for bark and
three inches for taper, per log; assuming
thst all logs are 14' long.
1 1.9"
138"
15.6"
17.3"
15"
18"
21"
24"
22 ft. b. m.
56 " "
106 " "
171 " "
29 ft. b. m.
78 " "
162 " "
277 " "
39 ft. b. m.
85 " "
184 " "
333 " "
18.9"
20.4"
21.9"
23.3"
27"
30"
33"
36"
253 " "
350 *' "
463 " "
591 " "
424 "
603 " "
813 " "
1054 " "
530 "
774 "
1066 " "
1404 " "
Mr. Snead recommends to measure the circumference outside the bark
at the big end and to divide the result by 4. He claims that the quotient
yields the diameter at the small end inside bark in such a way as to offset
mistakes made by Doyle, who underestimates small logs and overesti
mates big logs. Snead's suggestion is good, provided, that the cross sec
tion of the log is fairly circular, and that the difference between the small
diameter inside bark at the small end and the big diameter outside bark
at the big end, amounts to about 7 inches.
Diameter at small end
inside bark.
10 inches.
15
20
25
30
35
Contents of 16 foot logs, in feet b.m.
Doyle.
Snead.
Actual saw cut.
36'
8i'
70'
121'
169'
157'
256'
289'
279'
441'
441'
436'
676'
625'
628'
961'
841'
856'
The multiples of sectional area (derived from the diameter in inches,
but expressed in square feet) by length of log are readily obtained from
cylinder tables published by various authors. The log scale or log rule
used by the lumbermen (Lufkin rule) gives at a glance the contents of
logs 8 to 20 feet long, according to their diameter.
8 Forest Mensuration
PARAGRAPH XV.
UNITS OF LOG MEASUREMENT IN THE UNITED STATES.
The units of log measurement used in the United States differ greatly.
Graves' Handbook gives 43 "rules." The rules can be subdivided into
three main grops :
Board feet group (Par. XVI.) ;
Standard log group (Par. XVII.) ;
Artificial cubic foot group (Par. XVIII. ).
PARAGRAPH XVI.
BOARDRULES.
A foot board measure is a superficial foot one inch thick, in boards one
inch or more in thickness. It is a superficial foot, irrespective of thick
ness, in boards less than one inch in thickness.
The "board rules" merely guess at the number of feet board measure
obtainable from logs of a given diameter. The guess is based upon
either graphical considerations, circles of specified diameters being sub
divided into parallelograms 1% inch thick (diagram method), or else
on mathematical considerations, with a view to the fact that a cubic foot
of timber should theoretically yield 12 board feet of lumber, whilst the
actual loss for slab, saw kerf, etc., will reduce the output by 30% to
50%. In the Biltmore band saw mill, by over one thousand tests, the
actual loss for logs 12 inches to 40 inches in diameter has been found to
amount to 30%, or close to 1/3. Consequently, it is safe to say that the
band saw obtains from a cubic foot of log 8 board feet of lumber. *
The number of board feet which a log actually yields depends on:
1. The actual cubic volume of a cylinder having the length and small
est diameter inside bark of the log.
2. The defects of the log (heart rot, wind shake, bad knots, crooks),
which are usually eliminated by edger or trimmer.
3. The gauge of the saw, on which the saw kerf depends. The kerf
of band saws amounts to Y% inch, of circular saws to usually *4 inch, of
inserted tooth saws (of large diameter) to y% inch, of resaws to 1/16
inch.
4. The exactness of the work, especially depending on trueness of saw,
proper lining of saw and sawyer's skill ; further, on the exactness of the
setworks.
5. The thickness of boards obtained ; the minimum width of boards
permitted ; the amount of lumber wasted in the slabs ; shrinkage in drying.
The following table compares the contents of logs in cubic feet with
their contents in feet board measure as found by C. A. Schenck through
a thousand tests of actual yield in yellow poplar, as given by Doyle's
rule and by Lumberman's Favorite rule.
The figures given in columns c, f and i show the contents of a
log in feet board measure after Schenck's findings, Doyle's and Favorite
Forest Mensuration
9
rules. They are converted into cubic feet (columns d, g, and j) by divid
ing by 12. The loss incurred in sawing is shown by percentages (col
umns e, h, k) representing the ratio between the actual cubic con
tents of a log (as given in column b), and the cubic contents of inch
boards (columns d, g, j) obtained from such log.
It will be observed that the loss in the actual yield according to Schenck
forms a nearly constant proportion of the cubic contents of a log in the
case of all diameters, whilst, according to Doyle's and Favorite rules, the
figures of loss vary greatly.
The table refers to logs 12' long sawed into iinch boards.
Diameter
Contents.
Cubic
Schenck.
Doyle.
Favorite.
of
Log.
Feet.
Feet
Cubic
Loss
Feet
Cubic
Loss
Feet
Cubic
Loss
Inches.
b. m.
Feet.
0/
/o
b. m.
Feet.
%
b. m.
Feet.
%
a.
b.
c.
d.
e.
f.
g
h.
i.
j
k.
8
42
53
65
8.0
12
0.9
1.6
76
9
10
19
27
70
2.3
4.0
65
61
1 1
37
48
12
94
78
65
31
57
49
4i
56
13
11 .0
96
S.o
27
61
5i
54
62
52
53
14
12.8
112
93
27
75
63
5i
74
6.2
52
15
147
129
10.7
27
9i
7.6
48
90
75
49
16
16.8
146
12. 2
27
108
9.0
46
107
8.9
46
17
18.9
162
135
29
127
10.6
44
125
10.4
45
iS
21 .2
1 So
15.0
29
147
12.3
42
148
12.3
42
19
23.6
197
16.4
30
169
14. 1
40
170
14.2
39
20
26.2
212
177
32
192
16.0
39
186
155
41
21
28.9
230
19.2
34
217
18. 1
37
214
17.8
38
22
3i 7
248
20.7
35
243
20.3
36
243
20.3
36
23
346
266
22. 2
36
271
22.6
35
268
22.3
36
24
377
298
24.8
34
300
25.0
33
294
24 5
35
25
40.9
33i
27.6
32
33i
27.6
32
326
27.2
33
26
442
362
30.2
32
363
303
3i
35S
29. S
33
27
477
394
329
3i
397
33 1
30
390
32.5
32
28
513
422
352
3i
432
36.0
30
422
352
3i
29
550
456
38.0
3i
469
39 1
29
44S
373
32
30
58.9
488
40.7
3 1
507
423
28
474
395
33
3i
62.9
5i8
432
3i
547
456
27
509
42.4
33
32
67.0
556
46.3
3i
588
49.0
27
544
453
32
33
713
596
497
30
631
52.6
26
5S9
49.1
3i
34
757
634
52.8
30
675
56.3
26
634
52.8
30
35
80.2
670
558
30
721
60. 1
25
662
552
3i
36
84.8
710
592
30
768
64.0
25
690
575
32
37
89.6
755
62.9
30
817
68.1
24
734
61 .2
32
38
945
S06
66.7
29
867
72.3
23
778
64.8
3i
39
995
850
70.8
29
910
758
24
824
68.7
3i
40
104.7
901
750
28
972
81.0
23
870
72.5
3i
From column e it is evident that the bandsaw wastes close to 1/3
of the cubic contents of a cylindrical log, or 4' b. m. out of every cubic
foot.
Consequently, from hardwood logs 12 feet to 16 feet long, the band
io Forest Mensuration
saw will obtain the following actual number of feet b. m. (in 4/4"
thickness) :
D 2 X 0.78 X 12 X 8
(a) from 12 foot logs: , almost equal to D 2 X5
144
D 2
X 0.78 X 14 X 8
144
W
X 0.78 X 16 X 8
(c) from 16 foot logs: , almost equal to D 2 X7
144
Hence it can be stated generally, for logs of medium length "L," that
their contents in bandsawed inch lumber approximate
D 2 L — 2
— X feet b. m.
10 2
PARAGRAPH XVII.
STANDARD RULES.
_ Yv.M The standard rules do not estimate the contents of a log according to
output in board feet, but compare the log with a local average log. Such
average logs used to have, in the Northeast, formerly, a diameter of
either 19 inches (Adirondacks) or 22 inches (Saranac River) or 24
inches, and were in all cases 13 feet long.
The 19 inch standard log rule is known as Dimick's rule. Here the
"standard" or "market" is a log 13 feet long and 19 inches thick. On a
"b<\v, oi i.*f 22 jnch base ft j s T ^ f ee t long and 22 inches thick. On a 24 inch base
*"! <^ it is 13 feet long and 24 inches thick.
\ The standard contents of a given log are found by dividing the cubic
'volume of the standard log into the cubic volume of the given log.
d 2 X h
v (in standards) equals:
19 3 X 13
Scientifically and mathematically the standard rules are superior to
the board rules. One market, at a 19 inch base, is generally considered
equivalent to 200 board feet ; at a 22 inch base, to 250 board feet ; at a
24 inch base, to 300 board feet.
It is easily shown that the output of small logs is not as badly under
estimated, and the output of big logs not as badly overestimated on the
basis of standard rules, as is the case when Doyle's rule alone is applied.
PARAGRAPH XVIII.
CUBIC FOOTRULES.
In a third group of rules, a new unit, the "artificial cubic foot," is
introduced. This group of rules is established by law in Maine and New
Hampshire. (See Graves' Handbook, page 45.)
Forest Mensuration II
The artificial cubic foot corresponds with a log 12 inches long and
16 inches thick, which naturally contains 1.4 cubic feet. The rule as
sumes that 40/140 or 28.5% of a log goes to waste in the sawing process
as dust or slab.
To quickly transform artificial cubic feet into board feet, the laws pre
scribe certain arbitrary equivalents, instead of allowing 12 board feet
to equal one artificial cubic foot of timber. In New Hampshire, 10 board
feet equal one artificial cubic foot. In Maine, 11.5 board feet equal one
cubic foot. The rules might be used in connection with a cylinder table,
deducting 28.5% from the table data and multiplying the remainder by
10 or by 11. 5.
Remark : According to the Forest Reserve Manual, logs over 24 feet
long are treated as 16 foot logs and fractions thereof.
PARAGRAPH XIX.
EQUIVALENTS.
One cubic meter equals 35.316 feet or 1.308 cubic yards.
1,000 board feet of sawn lumber, 1 inch and more thick, correspond
with 2.36 cubic meters of sawn lumber.
A product of one cubic meter per hectar (2^2 acres) equals a product
of 14 cubic feet per acre.
One gallon equals 231 cubic inches in liquid measure, or 268.8 cubic
inches in dry measure (which is also l /2 peck).
One liter equals 1.0567 quarts; one cubic foot equals 74805 gallons
or 28.3 liters.
Logs yielding when split one cord of wood, will yield, when sawn:
For log diameter:
Feet board measure:
20"
25"
30"
35"
40"
515'
566'
605'
629'
649'
The Forest Reserve Manual adopts 2 cords as equivalent to 1,000
feet b. m., provided that the wood is split from timber 10 inches in diam
eter and over.
12 Forest Mensuration
Table Showing Relative Contents of Logs Without Bark.
Log diameter.
i cubic foot equals ft. b. m. Doyle
i cubic meter per nectar corre
sponds with ft. b.m. Doyle per
acre :
i cubic meter of log yields ft. b.
m. Doyle:
iooo ft. b. m. Doyle equal cubic
ft: _.
iooo ft. b. m. Doyle equal cubic
meters ! . . .
Artificial cubic feet per i ft. of log
No. of legal N. H. feet b. m. per
i ft of log :
Ft. b. m. Doyle per i ft. of log. . .
44.8
787.4
4.12
5768
86.
1455
218.
242.7
161.
6.87
•4
4
4
23
9
7
15'
6.2
73
102.2
258.8
1364
3.86
1.56
156
16.
25
8.09
113.26
285.7
123.6
35
245
245
275
30'
8.64
303
116
PARAGRAPH XX.
XYLOMETRIC METHOD.
The socalled "physical methods," by which the volume of a (partic
ularly irregular) piece of a tree may be accurately found, require either
the submersion of the piece in water (xylometric method) or the weigh
ing of the piece after finding its specific gravity (hydrostatic method,
§XXL).
The xylometric method can be applied in three ways, thus :
0. Submerge the wood in a graded cylinder partly filled with water
and find the water level before and after submersion.
b. Submerge the wood in a barrel partly filled with water; dip out
the water with a gallon measure until the water is as low as it was before
submersion. The number of gallons dipped out equals the volume of
the wood submerged. One gallon equals 231 cubic inches.
c. Place a piece of wood in an empty barrel of known contents ; fill
to the rim with water by the gallon. The difference between the known
contents and the number of gallons required gives the quantity of wood
in gallons.
In a, b and c it is necessary to use wood dry on the outside, to leave
the wood in the water a short time only, and to stir it up while in the
water so as to remove air bubbles.
PARAGRAPH XXI.
HYDROSTATIC METHOD.
The hydrostatic method deals with specific gravities. Specific gravity
is weight of an object divided by the weight of an equal volume of
Forest Mensuration
13
water. In the metric system, it equals weight in kilograms over cube
decimeters of volume. The specific gravity is found by weighing a given
body, and then weighing it again immersed in water. It equals weight
outside water over loss of weight submerged in water. The division of
the metric weight of a large body by the specfic gravity of a sample piece
yields the volume of the body in cubic decimeters.
Since wood is lighter than water, usually, a piece of lead must be
attached to the wood in order to submerge it. There must be ascer
tained :
1. The absolute weight of the piece of lead, H;
2. The weight of the same piece submerged in water, h ;
3. The absolute weight of the wood and of the lead, G;
4. The weight of wood and lead submerged in water, g.
The weight of the wood alone is, consequently, (G — H).
The specific gravity of the wood is
G — H
S ~(Gg)(Hh)
The volume, in cubic feet, of a quantity of wood weighing n pounds,
and having the specific gravity s, is
n 1 16n
volume = — X — =
s 63 1000s
The figure 63 represents the weight in pounds of one cubic foot of
water.
The specific gravity of wood is greatest close to the stump and in the
branches. For some species the outer layers show the greatest specific
gravity; for others the inner layers.
Species.
Spec, gravity,
air dry.
Weight of lumber per
1000 ft. b. m. in lbs.
Weight of one
cord in lbs.
White oak
Beech
Hard maple ....
Yellow pine ....
Spruce
White pine
•75
•7i
.66
•52
•45
•39
3900
3692
3432
2704
2340
2028
3985
3767
35io
2761
2391
2069
Rules to convert specific gravity into weight per 1,000 feet board
measure or into weight per cord read as follows :
1. Multiply specific gravity by 5,200. The result is the weight of
lumber per 1,000 feet board measure in pounds.
2. Multiply specific gravity by percentage of solid wood contained in
a stacked pile; then multiply the product by 8,050. The result gives the
weight per cord in pounds.
14 Forest Mensuration
FAllSXAPH XXII.
FACTORS INFLUENCING THE SOLID CONTENTS OF CORDWOOD.
>v The solid contents of wood stacks depend on the size and the form of
^r ^ the pieces composing them and on the method of piling. The solid con
<v. tents of a cord can be found only by the methods described in Para
graphs XX. and XXI. The European experiment stations have collected
"•^^V^^^^^data to that end on a very large scale, and have established the following
.^p^ laws :
^^Vvaav^^ a. The bigger the pieces of wood in a stack, the larger are the solid
_vv^^^~^~~ contents of the stack.
X»~ ^m^avtj^j^ £. The longer the pieces of wood, the smaller are the solid contents
of the stack.
' c. Pieces piled parallel and tightly greatly increase the solid contents
of the stack.
d. During the drying process, hardwoods shrink approximately by
<s^J_^^^ 12%, and soft woods by 9%. The shrinkage is partly offset by the
n ^ cracking of wood.
These rules are important in the pulp, tanningwood and firewood trade.
PARAGRAPH XXIII.
REDUCING FACTORS FOR CORDWOOD.
The countries using the metric system pile wood in space cubic meters.
One space cubic meter equals .274 cord. The pieces contained "therein
are 3.28 feet long. For such conditions the following figures hold good :
a. First class split wood, obtained from sound pieces 12 inches in
diameter, contains per cord 102.4 cubic feet of solid wood (reducing fac
tor 80%).
b. Composed of inferior split wood, obtained from round pieces having
a diameter of 6 inches, a cord contains 96 cubic feet of solid wood (re
ducing factor 75%).
c. In heavy, round branch wood (diameters of about 6^ inches)
87 cubic feet of solid wood are found in a cord (reducing factor 68%).
d. In round pieces of branch wood, 4 inches in diameter, yy cubic
feet are found in a cord (reducing factor 60%).
e. In faggots, 25 to 51 cubic feet make a cord (reducing factor 20%
to 40%).
The percentages for broad leafed species are smaller than those for
conifers, owing to the latter's straight growth.
At Biltmore, one cord of 8 foot split oak contains about 80 cubic feet ;
one cord of kindling finely split about 90 cubic feet; one cord of blocks
12 inches long about 100 cubic feet of solid wood.
Forest Mensuration 15
In the sale of tannin wood it is well to sell 5 foot sticks finely split
rather than heavy blocks 4 feet long.
In the sale of pulp wood, 12 foot sticks yield much higher returns than
4 foot sticks, if sales are made by the cord.
PARAGRAPH XXIV.
LOCAL PECULIARITIES WITH REFERENCE TO STACKED WOOD.
Tannin and pulp wood industries sometimes figure at a cord containing
160 stacked cubic feet, equal to \V\ ordinary cords of 128 stacked cubic
feet.
After Graves (page 65), a cord of firewood is in certain sections under
stood to be 5 feet long, 4 feet high and 6^2 feet wide.
Under "a cord foot" is understood a stack 1 foot by 4 feet by 4 feet
(% cord or 16 stacked cubic feet).
Under "a cylindrical foot" is understood a stacked cubic foot equal
to 1/128 cord. The number of such feet (a misnomer for stacked cubic
feet) in a stick is
d*Xl
144
(/ equals length of stick in feet; d equals its diameter in inches).
In New England, a cord of pulp wood is sometimes measured by
calipering the round sticks composing it, and tables are constructed to
facilitate calculation. Proceed as follows :
Ascertain diameter of sticks in inches, square them singly, total the
results and divide by 144. Multiply the quotient by length of sticks in
feet and divide by 128.
PARAGRAPH XXV.
BARK.
Bark is usually sold and bought by the cord. The tanneries, however,
instead of measuring a cord of 128 cubic feet, apply the misnomer "one
cord" to a weight of 2,240 lbs. (the long or European ton).
Twelve cords of bark fill one common (old) freight car.
A stack of bark contains from 30% to 40% solid bark. The specific
gravity of fresh oak bark is 0.874; dried, it is 0.764.
The bark of white oak has been found (at Biltmore), to comprise:
In trees 20 years old, 55% of the wood, or 35% of the whole bole ;
In trees 60 years old, 41% of the wood or 28% of the whole bole;
In trees 100 years old, 29% of the wood or 22% of the whole bole ;
In trees 140 years old, 21% of the wood or 17% of the whole bole.
i6
Forest Mensuration
Chestnut oak peeled at Biltmore yields the following results per tree,
arranged according to the diameter of the trees 4 l / 2 feet above ground:
Diameter of tree
Dry Bark in
Kilogram = r ^^ cord, per Tree.
chest high in inches.
Minimum
Average.
Maximum.
6
5
13
27
7
6
17
36
8
8
24
48
9
12
33
61
IO
18
45
77
ii
26
60
95
12
37
73
114
13
50
88
135
14
65
105
158
15
81
126
180
16
98
150
204
17
116
172
234
18
136
195
266
19
159
224
3H
20
181
250
365
21
205
275
22
230
305
23
265
336
24
275
375
If the percentage of bark in a log or tree (scaled with the bark) is
p, then the bark percentage in ratio to the solid wood alone is :
100 X p
100 — p
According to thickness of bark and diameter of logs, the following
percentages can be given for the ratio :
bark
bark plus timber
Diameter with
Thickness of bark.
bark — inches.
\"
1"
1 4"
2"
10
15
20
25
30
19%
12%
9%
7%
6%
36%
24%
19%
15%
12%
51%
36%
27%
22%
19%
64%
46 %
36%
29%
24%
Forest Mensuration 17
SECTION II.— VOLUME OF STANDING TREES.
PARAGRAPH XXVI.
METHODS OF OBTAINING THE VOLUME OF STANDING TREES.
The volume of standing trees may be ascertained
By estimating it (Par. XXVII.) ;
By measuring heights and diameters (Par. XXVIII.) ;
By the form factor method, which combines estimates and meas
urements (Par. XXIX. f. f.).
By these means can be obtained the volume of the bole (from roots to
top bud), or the volume of saw timber in any of the 43 log scales, or
the volume of firewood in cords, etc., or the total volume, including brush
and roots.
Under "used volume,"' Circular 445 of the United States Bureau of For
estry understands the sum of the volumes of logs cut from a tree ; under
"merchantable volume" the total volume of that portion of the tree which
is merchantable under certain conditions.
PARAGRAPH XXVII.
HELPS AND HINTS TO FIND THE VOLUME OF STANDING TREES.
It is difficult to estimate the cubic contents, wood contents or lumber
contents of a standing tree. In the case of estimates in board feet, the
result depends on the exclusion or inclusion of crooked and defective
pieces, on the taper of the bole, on the soundness of the heart, and on
the minimum diameter admissible in the top log. Compare end of Par
agraph XXXII.
Most hazardous is the volume estimate of overaged trees, especially
in the case of hardwoods (chestnut).
The following helps might guide the novice :
1. The volume of a sound tree bole, in cubic meters, is equal to
1000
for example, diameter (breast high) 30 c. m. ; contents 0.9 cubic meters.
2. The contents of a standing tree, in cubic feet, are about
10
for example, diameter (breast high), 25 inches; contents (from butt to
tip), 125 cubic feet.
3. The number of feet Doyle in a tall sound tree equal
3
— D 2
2
1 8 Forest Mensuration
for example, diameter (breast high), 20 inches; contents 600 feet board
measure.
4. The contents of a tree in feet Doyle approximate, assuming that
the bole is cut into 16 foot logs, and that the tree tapers 2 inches per log :
N X D (D— 12)
wherein N represents the number of logs obtainable; D the diameter of
the butt log without bark at breast height.
5. The cordwood contained in a sound bole is :
D 2
X C
1000
wherein C amounts to :
1.5 in the case of trees 8" through ;
2.0 in the case of trees 16" through ;
2.5 in the case of trees 24" through.
PARAGRAPH XXVIII.
SCIENTIFIC METHODS OF ASCERTAINING THE CUBIC CONTENTS OF STANDING
TREES BY MERE MEASUREMENT.
The cubic volume of the bole, on the basis of diameter measurement
and height measurement, in the case of a standing tree, may (with the
help of climbing iron, ladders, camera or instruments constructed for
the purpose) be figured out: ► .
1. According to the formulas of Hossfeldt, Riecke and Simony. In
this case, the upper diameters must be measured indirectly.
2. According to Huber's and Smalian's formulas, the diameters of
equal sections of the trees being indirectly measured.
3. According to Pressler's formula, which is, for the volume of the
bole lying between chest height and top bud, 2/3 of sectional area "S"
at chest height times "rectified" height of bole. The rectified height "r"
is the distance of chest height from that point of the tree bole which
has l / 2 of the chest height diameter (from the "guide point"). The
equation 2/3 r x S holds good for paraboloid, cone and, at a slight mis
take, for the neilloid.
The volume of that part of the tree bole which lies below chest height
is ascertained (as a cylinder) as being equal to sectional area chest high
times 4.5.
Remark : 4.3' is the chest height usually recognized by the authors ;
Pinchot adopts 4.5'.
The Pressler formula does not hold good for truncated boles.
Forest Mensuration 19
PARAGRAPH XXIX.
FORM FACTOR METHOD.
The form factor or form figure method relies on the measurement of
the sectional area — usually the one at breast height, — the measurement
or the estimation of the total height and the estimation of the form
figure.
The form factor is a fraction expressing the relation between the actual
contents of a tree, in any unit, and the ideal contents which a tree would
have if it were carrying its girth (like a cylinder) up to the top bud
undiminished.
The form factor may be given in reference to the volume of the entire
tree, inclusive of branches in cubic feet ; or in reference to the volume
of the bole only ; or in reference to the merchantable part of the bole ;
in the latter case either in feet board measure or in standards or in cords.
Historic Remarks : Some of the older authors on mensuration saw in
the cone and not in the cylinder the ideal form of the tree, basing their
s X h
form factors on the ideal volume .
PARAGRAPH XXX.
KINDS OF FORM FACTORS MATHEMATICALLY.
Scientifically we distinguish between :
1. The absolute form factors which have reference only to the volume
standing above chest height. They can be readily ascertained with the
help of Pressler's formula. Generally speaking, V equals Sx H x F.
After Pressler, V equals S x 2/3 x r; thus *— equals F.
H
For the cone the absolute form factor is onethird ; for the neilloid
onefourth ; for the paraboloid onehalf, whatever the height of the tree
may be. Hans Rienicker, the author of these form factors, finds for
trees up to 50 years old a form figure of 35% to 43% (in regular, dense
German woods); in trees 50 to 100 years old, F increases up to 50%;
thereafter occurs a slight decrease below 50%.
2. The normal form factors which were recommended by Smalian,
Pressler and other oldtime authors. They have reference to the entire
volume and necessitate the measurement of the diameter at a given frac
tion (usually 1/20) of the total height of the tree. Frequently, in case
of tall trees, the point of measurement cannot be reached from the ground.
The bole form factor for diameters measured at 1/20 of the height is :
For a paraboloid, 0.526 ; for a cone, 0.369 ; for a neilloid, 0.292. These
form factors, like the absolute form factors, are independent of the height.
3. The socalled "common form factors" which do not express, as a
matter of fact, the form of the tree, since they do not bear any direct
ratio to the degree of the tree curve. They should be termed, more
20
Forest Mensuration
properly, "reducing factors." These form factors alone are nowadays
practically used. They are based on diameter measurements, chest high,
and have reference not merely to the bole of the tree, but as well to any
parts of the bole, to root and branch wood, to saw logs, etc. These form
factors depend entirely on the height. If, for instance, a paraboloid is
one rod high, the form factor is 0.673 ; and if it is 8 rods high, the form
factor is 0.517.
PARAGRAPH XXXI.
KINDS OF COMMON FORM FACTORS IN EUROPEAN PRACTICE.
The following kinds of form factors may be distinguished :
1. Tree form factors. The tree is considered as bole plus branches.
2. Timber form factors. The term timber, in Europe, includes all
parts of the tree having over 3 inches diameter at the small end.
3. Bole form factors. Bole is the central stem from soil to top bud.
For America, form factors would be of great value ascertained by exact
measurements and arranged according to diameter, height and smallest
log diameter used.
Tables of form factors may be constructed, for instance, for shortleaf
pine, on the basis of Olmsted's working plan, pages 1733.
PlNUS ECHINATA.
Diameter.
Merchantable length
Cubic feet
Form fig.
Contents
of bole.
Ideal cylinder.
b. m. Doyle.
16"
36'
50.3
36
* 180'
18"
47'
83
1
3
6
300'
20"
5i'
112
1
4
440'
22"
56'
147
8
4
600'
24"
59'
185
3
4
2
780'
26"
61'
224
9
4
4
980'
28"
62'
263
1
4
5
1 190'
3o"
62' 6"
306
7
4
6
1420'
32"
63'
35i
8
4
7
1680'
34"
63' 6"
400
3
4
8
1930'
36"
64'
457
3
4
9
2200'
The influence of age, soil, density of stand, height, diameter and
species on the various form factors, with cubic measure as a basis, has
not been fully ascertained.
For the tree form factor, the most important influence, in the case of
trees less than 150 years old and raised in a close stand, seems to be
that of the height of the tree ; with increasing height the tree form factor
decreases — c. g., for Yellow Pine :
One pole high 93
Two poles high 65
Four poles high 53
Six poles high 49
Forest Mensuration 21
The timber form factor, based on cubic measure of a tree, rises with
increasing age and increasing height up to a certain point (for Yellow
Pine at 3 poles), provided that the term timber includes all stuff over
3 inches in diameter. The timber form factor is a function more of
the diameter than of the height. Timber form factors of Yellow Pine
are :
Trees 1 pole high 07
Trees 2 poles high
Trees 3 poles high
Trees 4 poles high
Trees 7 poles high
The timber form factor in shade bearers is a little higher than that
in light demanders (within an age limit of 150 years, for trees in close
stand).
The bole form factor can be found, in fact, only for species forming
a straight bole free from large branches (hence especially for conifers).
The bole form factors, to begin with, are large ; with increasing height,
they decrease gradually to a par with the timber form factors — e. g., for
Yellow Pine :
1 pole high 70 3 poles high 49
2 poles high 55 4 poles high 47
7 poles high 45
European common form factors are collected by thousands of measure
ments taken in a large variety of localities. It must be remembered that
a form factor read from a table is never applicable to an individual tree,
and is only applicable to an average tree amongst thousands.
For trees less than 120 years old, the branch wood (stuff less than 3
inches in diameter) comprises from 15% to 28% of the entire tree vol
ume; this figure, in the case of broadleaved species, rises from 25% up
to 33%. For trees as now logged in America, the branchwood percentage
is naturally very much smaller.
The tree form factor equals stump plus bole plus branches
ideal cylinder
The timber form factor equals all stuff having over 3" diameter
ideal cylinder
The bole form factor equals bole from ground to tip
ideal cylinder
By form height is meant the product of height (total height of tree)
times form factor, or else that much of the height of the ideal cylinder
which the tree volume, poured into the ideal cylinder, would fill. Since
the form factor on the whole decreases with increasing height, the form
height is a fairly constant quantity; at least for trees of merchantable
size. Hence the helps and hints given in Paragraph XXVII (to quickly
find the volume of standing trees from mere diametermeasurement) may
22 Forest Mensuration
%
lay claim to correctness in many cases. For instance : The cubic con
tents of a tree are supposed to be equal to
tt D 2 X H X F
X ■
4 144
After Paragraph XXVIL, 2, these contents are also
2
—X D 2
10
B
= D 2 X 78 X H X F
5
288
H X F = =37
7.8
As a matter of fact, the form height of trees I foot to 2 feet in diam
eter is close to 2>7 And for such trees the equation holds good.
The form height may also be defined as "volume (standards, cords,
bark, etc.) per square foot of sectional area chesthigh."
PARAGRAPH XXXII.
MEANS FOR EXACT MENSURATION OF STANDING TREES.
The means used to find the exact solid volume of standing trees are
instruments for measuring the total height of the merchantable length
of a tree ; instruments for measuring the diameter at given heights ; fur
ther tables based on scientific research and experience, or tables merely
meant to facilitate calculation. Instruments for measuring diameters far
above ground are needed for the use of the formulas given by Riecke,
Hossfeldt, Pressler, etc.
The six paragraphs following next dwell upon these topics.
PARAGRAPH XXXIII.
MEASURING THE HEIGHT OF A STANDING TREE.
The height of a tree can be measured by comparing its shadow with
the shadow of a stick, say io feet long. The "Lumber and Log Book"
gives another old method (page 133) of height measurement. If the
observer places himself in such a way that a small pole stands between
him and the tree at a distance e, and if he marks on the pole two points
where his sight, directed towards the top and base of the tree, touches
the small pole, and if he further ascertains the distance E separating him
from the tree, then the height of the tree H equals
E
— X h
e
wherein h represents the number of feet between the two points marked
on the pole.
Forest Mensuration 23
I
Instruments (hypsometers) for height measuring are sold in many
forms. The following are frequently used: Rudnicka's instrument; Press
or's "Measuring Jack;" Faustmann's "Mirror Hypsometer;" Weise's Tel
escope ; Kcenig's "Measuring Board ;" Brandis' "Clinometer ;" Klausner's
instrument ; Christen's "Non plus ultra."
Compare Woodman's Handbook, pages 136 to 137, for staff method;
page 138 for Faustmann's; page 140 for tangential clinometer; page 143
for mirror clinometer.
Christen's stick is not accurate enough for the measurement of trees
over 100 feet high. It does not require the measurement of distances. Its
form is improved by Pinchot.
PARAGRAPH XXXIV.
FACTORS INFLUENCING THE EXACTNESS OF HYPSOMETRICAL OBSERVATIONS.
The best results are obtained if the distance between tree and observer
equals the height to be measured. In sighting towards the spreading top
of a hardwood tree, the observer is apt to overrate the height, the tip
being buried in the spreading crown. The line of sight strikes the edge
of the crown instead of striking the apex of the crown.
Timber cruisers are usually satisfied to determine the number of logs
obtainable from the bole instead of determining the length of the bole.
As a matter of fact, where the tree furnishes saw logs only, the total
height of the tree is a less reliable indicator of the total contents than
the length of the merchantable bole.
Instruments like Faustmann's, Kcenig's and Pressler's cannot be used
in windy and rainy weather. Dense undergrowth and dense cover over
head render exact measurement impossible.
PARAGRAPH XXXV.
INDIRECT MENSURATION OF DIAMETERS.
The following instruments are used to measure the diameter of the tree
at any point of bole :
a. Winkler, an addition to Kcenig's measuring board.
b. Klausner.
c. An ordinary transit.
d. Wimmenauer's telescope.
PARAGRAPH XXXVI.
PRESSLER'S TELESCOPE.
Pressler's telescope is used to find the "guidepoint" and the "rectified
height," as defined in Paragraph XXVIII., 3. The diameter chesthigh
is taken between the nails at the end of the instrument. Then the tele
scope is pulled out to a length double the original, divided by the cosin
24 Forest Mensuration
of the angle found between the horizon and the probable sight to the
"guidepoint" (at which the observer expects to find onehalf the diameter
chesthigh). Thus, actually, the instrument merely examines the correct
ness of an original estimate.
The Pressler telescope can be used for finding the merchantable length
of any bole. Merely place a stick, equal in length to twice the minimum
diameter permissible in a merchantable log, at the foot of the tree, catch
it between the nail points and proceed as described.
PARAGRAPH XXXVII.
AUXILIARIES FOR CALCULATION.
Auxiliaries for calculation are :
1. Sectional area tables (Schlich, Vol. III.); engineering books like
Haswell's; Bulletin 20; also Green.)
2. Ideal cylinder tables (Schlich and Bulletin 20).
3. Multiplication tables and logarithmtables.
4. Tables showing contents of logs in any of the 43 rules, according
to length and diameter.
PARAGRAPH XXXVIII.
TREE VOLUMETABLES.
Tree volume tables have been constructed on a very large scale for the
leading species in the old country. In the United States, the Government
is now beginning to make such tables. The tables give the cubic, dumber
and cord wood contents of trees, according to species, diameter and some
times according to total height and merchantable height (number of logs).
Bulletin 36 reprints the following tree volume tables :
A. According to diameter measure merely.
Page 92. Adirondack White Pine, volume in standards.
Page 94. Pennsylvania Hemlock, volume in feet, b. m., Scribner.
Page 94. Adirondack Hemlock, in standards.
Page 95. Adirondack Spruce in standards.
Page 96. Adirondack Birch, Beech, Linden, Sugar Maple in Scribner,
feet, b. m.
Page 96. Adirondack Balsam, in standards.
Page 97. Adirondack White Cedar, in standards.
Page 98. Arkansas Shortleaf Pine, in feet, b. m., Doyle.
Page 98. Missouri Ash, Elm, Maple, Cypress, Gum, Oak, Hickory,
Poplar, in feet, b. m., Doyle.
Page' 99. Western Yellow Pine, in feet, b. m., Doyle (Black Hills), dis
tinguishing between the volume of first and second growth.
Page 99. Yellow Poplar in Pisgah Forest in feet, b. m., Doyle, distin
guishing between good, average and poor conditions of
growth.
Forest Mensuration 25
All tables, except Yellow Poplar tables, are based on the measurement
of a large number of trees. The Yellow Poplar tables are based on stem
analyses of a small number of trees.
B. According to measurement of height and diameter combined.
Page 93. Wisconsin White Pine (height expressed by the number of
logs obtainable from merchantable bole) in feet, b. m., Doyle.
Page 103. Adirondack Spruce expressed in feet, b. m., Scribner, the
total height of trees being measured.
Page 104. The same in cubic feet.
Page 105. The same in cords for pulp wood.
Page 106. New Hampshire Spruce in feet, b. m., in New Hampshire
cubic feet sanctioned by law.
Pages 108 and ill. Adirondack White Pine with bark, expressed in
cubic feet.
Page no. Adirondack White Pine in feet, b. m., Doyle.
Monographic investigation into the growth of the leading American spe
cies is of great importance. The trees of virgin forests are very defective,
however, and tree tables can never be constructed giving the contents of
defective trees.
SECTION III.— VOLUME OF FORESTS.
PARAGRAPH XXXIX.
SYNOPSIS OF METHODS FOR ASCERTAINING THE VOLUME OF FORESTS.
The methods used to find the volumes of entire forests, of forest com
partments, tracts, quarter sections, coves, etc., are :
1. Estimating (Par. XL.).
2. Exact calculation after measurements (Par. XLI., f. f. ).
3. Combined measuring and estimating (Par. IL., f. f.).
Obviously, measuring without estimation is possible only in forests con
taining little unsound timber.
PARAGRAPH XL.
ESTIMATION OF FOREST VOLUME.
In primeval woods, where a few assortments only are salable and where
stumpage is cheap, the estimation of stumpage necessarily takes the place
of the measurement. If any measurements are taken, they are merely
meant to back the estimation of the cruiser. The more defective the trees
are, the more preferable is judgment and local long experience in the mill
and in the woods on the side of the cruiser to mere measuring.
26 Forest Mensuration
The volume of a wood is ascertained by cruisers' estimates in the fol
lowing ways :
a. By estimating the number of trees and the volume of the average
tree with due allowance for defects.
b. By counting the trees and estimating the volume of average trees
with allowance for defects.
c. By estimating the volume of each tree separately, sounding it with
an axe, when necessary, and judging its soundness from all
sides.
The above methods (a, b, c) are applied either to sample plots or to
sample strips or to the entire area.
A blazing hammer is often used to prevent duplication; the revolving
numbering hammer might be used in case of scattering trees, so as to
allow of control of the estimates by the owner, his forester or the pros
pective purchaser of stumpage.
In irregular forests — hardwood forests of the United States — the only
safe way is separate estimating of each individual tree after careful in
specting. Incredible errors result from wholesale and rapid estimates.
In the case of even aged woods, a look at the height growth and a
knowledge of the age gives a good idea of the forest's volume. Under
very poor conditions of growth, the annual timber production per acre
and year is as little as 15 cubic feet; under the best conditions it is as
much as 250 cubic feet per acre and year. On an average (on absolute
forest soil), 50 cubic feet per acre and year may be considered as the
production of healthy and densely stocked forests.
PARAGRAPH XLI.
PRINCIPLES UNDERLYING THE EXACT MENSURATION OF FOREST VOLUME.
The basis of any exact measurement of volume is formed by a survey
of the sectional area, combined with an account of the number of stems ;
sectional area and number are found by calipering (valuation survey).
Whatever rule of log measurement may be at stake, the total sectional
area of the forest is always of first importance for a survey of forest
volume. Next in importance is the calipering of sample trees, followed
by an exact survey of their volume. The ratio r existing between the
volume of the sample trees (expressed in any unit or mixture of units)
and the sectional area of the sample trees is identical with the form
height (compare Par. XXXII., towards end) of the sample trees. The
form height of sample trees properly selected is the form height of the
forest. The sample trees are usually cut and worked up into logs, cord
wood, tannin wood, etc., for the purpose of volume survey.
V v f. h. s.
— — _ = and V — S. f. h
S s s
Forest Mensuration
27
If the trees of the forest are defective, the sample trees should exhibit
average defects.
PARAGRAPH XLII.
FIELD WORK FOR EXACT VALUATION SURVEYS.
The valuation survey requires :
1. Calipering of all trees; the diameter is taken in inches or in multi
ples of inches. Each species and each height class or age class are or
may be taken separately.
2. Entering the takings on tally sheets, arranged as follows :
Diameter.
Spruce.
Beech.
Height classes.
Height classes.
I
II
I
II
10"
n"
12"
13"
etc.
The larger the trees are, the bigger is the permissible interval of
calipering. If trees average two feet in diameter, an interval of 3 inches
is permissible, provided that a large number of trees are calipered.
It is a strange fact that the diameter measured from east to west is
larger on the whole than the diameter from north to south.
PARAGRAPH XLIII.
BASAL ASSUMPTIONS.
The only assumption made in calculating the volume of the forest after
Paragraph XLI. is that the form height of the sample trees equals the
form height of the forest. No other estimate or assumption is being
made. This premise is much safer than the assumption that the volume
of the forest bears the same ratio to the volume of the sample trees
which the number of trees in the forest bears to the number of the sample
trees. More unsafe is the assumption that the volumes of forest and
sample trees bear the ratio of the acreage occupied by the forest on the
one hand and by the sample trees on the other hand.
28
Forest Mensuration
PARAGRAPH XLIV.
SELECTION OF SAMPLE TREES.
Sample trees are selected either irregularly or after a regular plan. In
the latter case, it is best to distribute them equally among the diameter
classes composing the forest (DraudtUrich method and Robert Hartig
method), instead of selecting sample trees of average diameter.
It is more important that the sample trees should have proper average
classform height (and average defects) than that they should have exact
average classdiameters.
PARAGRAPH XLV.
DRAUDTURICH METHOD.
The DraudtUrich method is in common use abroad for measuring
the forest. The trees of the forest are divided into a number of classes
(usually five). Each class contains an equal number of trees, class I
containing the largest and class 5 the smallest trees. In each class an
equal number of sample trees, having about the average diameter of the
class, are felled and worked up into logs, cordwood, ties, poles, etc. The
form height of all sample trees is obtained as the quotient of their volume
(in any unit or mixture of units) divided by their sectional area. Mul
tiplying the sectional area of the forest with this form height, the exact
volume of the entire forest and its composition (logs, poles, cords, etc.)
are given by one operation.
Sample trees of the average diameter of a class are found by dividing
the sectional area of the entire class by the number of trees per class. It
is wrong to find the average diameter by dividing the sum total of the
diameters by the number of trees.
Diameter
Breast High.
Number
of
Trees.
Diameter
Classes
of Trees.
Number
of Sample
Trees.
Average Diam
eter of Sample
Trees.
40"
35"
30"
25" 
20"
15" j
(
10" \
1
310
240
506
1226
I
1 1
29"
9
1040
1233
II
1 1
17"
1847
435
III
1 1
14"
2282
IV
1 1
10"
!
1
2282
V
1 1
10"
Forest Mensuration 29
The advantages of the DraudtUrich method are :
r. All sample trees can be worked up in a bunch.
2. Not only the entire volume but as well the different grades of tim
ber, fuel, ties, etc., composing the volume are found by one operation.
A large number of sample trees are, however, required, and, since the
volumes of the various classes are unequal, a negative mistake made in
establishing the volume of one class is not apt to be counterbalanced by
a positive mistake made in finding the volume of another class.
PARAGRAPH XLVI.
ROBERT HARTIG METHOD.
Robert Hartig's method forms tree classes containing equal sectional
areas— not equal numbers of trees. An equal number of sample trees is
cut in each class and worked up separately for each class. The volume
of the forest is also obtained separately for each class. Otherwise, the
manner of proceeding is identical with that of Paragraph XLV.
Preferable it would seem to cut in each class a number of sample trees
having, in the aggregate, the same sectional area. This scheme, how
ever, would represent the bigdiameter class by an absurdly small num
ber of samples.
PARAGRAPH XLVII.
AVERAGE SAMPLE TREE METHOD.
If average trees of the entire rorest are taken as samples, then the
volume of the forest is obtained with smaller accuracy.
The proportion which the different assortments of timber, wood, bark,
etc., form in the entire output is not clearly shown by such sampling.
In a normal, evenaged wood the tree of average cubic volume is found
by deducting 40% from the total sectional area, beginning with the de
duction at the biggest end. The largest tree then left is, or happens to
be, the average tree of the wood.
PARAGRAPH XLVIII.
EXACT MENSURATION WITHOUT CUTTING SAMPLE TREES.
Frequently the cutting of sample trees for the purpose of a valuation
survey is not feasible. The volume of the forest in cubic feet — but not
the assortments composing the volume — may then be ascertained as fol
lows :
a. Take the total sectional area of the forest according to diameters
and species and, if necessary, according to height classes.
b. Ascertain the bole volume of some available trees with the help of
Pressler's tube or by indirect measurement of heights and diameters.
30 Forest Mensuration
c. Proceed as indicated in the last three paragraphs, keeping in mind,
however, that only the cubic volume of the boles is thus obtainable. The
branchwoodpercentage or the timberpercentage of the bole must be
estimated.
The Hartig method (Paragraph XLVI.) might be combined with the
use of Pressler's telescope, and the bole volume of a wood above breast
height might be ascertained as 2/3 of the total sectional area of the
forest, multiplied by the arithmetical mean of the rectified heights of
the sample trees representing the various diameter classes.
2 S (r t + r 2 + r3 + r 4 + r„)
V = X
3 5
The bole volume below breast height in cubic feet is equal to the
sectional area of the wood times 4J/2.
PARAGRAPH XLIX.
COMBINED MEASURING AND ESTIMATING.
If measuring and estimating are combined, the following typical meth
ods may be used to ascertain the volume of woods :
1. The form factor method (Paragraph L.).
2. The form height method (Paragraph LI.).
3. The volume table method (Paragraph LIL).
4. The yield table method (Paragraph LIIL).
These methods might be used in connection with the socalled "dis
tance figure" of Paragraph LIV.
In applying these methods, one or the other of the three factors of
volume (sectional area, height and form factor) are obtained by estima
tion.
The paragraphs following Paragraph LVIII. give a number of methods
practically used and also based on combined measuring and estimating.
PARAGRAPH L.
FORM FACTOR METHOD.
The form factor method ascertains the sectional area by calipering,
according to species, and, if necessary, according to height classes. The
average height of the wood (by species, classes) is obtained by actual
hypsometric measurement. The form factor is read from local form
factor tables.
The average height is obtained — not as the arithmetic mean of a num
ber of heights measured, but much more — correctly from the ratio exist
ing between the sum total of the ideal cylinders and the sum total of
the sectional areas of the trees hypsometrically measured. The form
factors appearing in form factor tables must be averages obtained by
many hundreds of local measurements.
Forest Mensuration 31
Mistakes amounting to up to 25% in the sum total of the volume
obtained by the form factor method are not impossible, since average
form factors appearing from a form factor table are often at variance
with the actual form factor.
Form factor tables for American "second growth" are still lacking. In
primeval woods the form factor method seems out of place.
PARAGRAPH LI.
FORM HEIGHT METHOD.
The form heights of merchantable trees are, generally speaking, sub
ject to only small variations. Those, e. g., for Adirondack White Pine
scaling from 18" to 36" in diameter breasthigh are (for standard rule)
close to 1.25.
Multiplying the sectional area of a White Pine woodlot (say 100 square
feet) by the form height previously obtained through official measure
ments (like those by T. H. Sherrard), the volume of the woodlot — in
the present example about 125 standards — is easily obtained.
Form height tables based on feet b. m., Doyle, are not as simple as
those based on the standard rules and cubic foot rules, owing to the
mathematical inaccurary of Doyle's rule, which causes the form heights
to be preeminently dependent on the diameters.
Form height tables should be constructed for the leading merchantable
species in the United States. Of course, such tables are more readily
applicable to second growth than to first growth.
The form height tables should exhibit the number of standards, cords,
ties, etc., obtainable per square foot of sectional area in each diameter
class. In case of defective trees, proper allowance must be made for
defects — rather a hazardous risk in primeval hardwoods.
PARAGRAPH LII.
VOLUME TABLE METHOD. \^_l3<S <Fv WaX /0^^i_vj ' V
In Paragraph XXXVIII. a number of volume tables have been enum
erated, from which the volume of trees of given species and diameter
(and height) can be readily read.
A valuation survey of the forest (or of a woodlot or of a sample plot)
yields the diameters of the trees stocking thereon. The number of
trees found for each diameter class is multiplied by the contents of a
tree of that diameter appearing from the volume table. The sum total
of the multiples is the sum total of the volume of the forest.
32
Forest Mensuration
Sample.
u
+J
B
Yellow Pine.
Hickory.
Oak.
03
s
No.
trees.
Average
volume.
Total
volume.
No.
trees.
Average
volume.
Total
volume.
No.
trees.
Average
volume.
Total
volume.
12
15
18
21
24
27
30
33
36
30
42
17
36
33
20
10
1
1
60
I20
300
520
780
1080
1420
1800
2200
I .800
5.040
5.IOO
18.720
25.740
2 I . 600
14. 200
1 . 800
2 . 200
7
9
18
5
12
6
3
140
240
370
500
660
840
1050
980
2160
6600
2500
7920
5040
3150
14
5
23
22
22
7
10
5
5
160
200
350
520
730
940
1 1 50
1400
1800
I .400
I .OOO
8.050
1 1 . 440
i 6 . 060
6.580
1 1 . 500
7 .000
9.000
Totals .
96 . 200
28.350
72.030
Grand total 196.580' B. M.
The volumes of the column "Average Volume" are taken from tables
published by the Bureau of Forestry.
PARAGRAPH LIII.
YIELD TABLE METHOD. r>sv
^XXV. ^M^x
^
All over Europe local yield tables are used to quickly ascertain the
volume of pure, sound, even aged woods. For America, such yield tables
— normal local yield tables — exist only in the white pine tables given in
Pinchot and Graves' pamphlet, "The White Pine."
The method of construction of yield tables appears, from Paragraph
XCII. and following.
Under yield tables are understood "acrevolumetables," whilst under
volume tables are understood "treeyieldtables."
Normal yield tables specify the age of even aged and pure woods, the
height of such woods and the volume (by assortment) of such woods,
according to the productiveness of the soil. An indication for the latter
is found in the height growth.
Such yield tables hold good only for woodlots normally stocked. A
woodlot is normally stocked "when all local factors of wood production
have pronounced themselves unhampered in the annual production of
fibre." Normal woods, even of small extent, are extremely rare. In Ger
many the average wood lacks 25% of being normal. Since the normal
yield tables give the yield for normal conditions only, a deduction must
be made from the volume indicated by the yield table when applied to
a given woodlot, according to the abnormality of the same.
Proceed as follows :
Forest Mensuration 33
Ascertain age and average height of the trees ; find the yield table
which gives a similar height for the same age; reduce the volume indi
cated by this yield table and for this age, by estimating the deficiency of
the growing stock.
Obviously, there is much room for guessing, since neither height nor
form figure nor sectional area in woodlots abnormally stocked can lay
claim to normality.
Schuberg, denying a truism otherwise generally acknowledged, claims
that the height alone does not indicate the productiveness of the soil.
At present, normal yield tables are of little use in American forestry.
PARAGRAPH LIV.
DISTANCE FIGURE.
Under "distance figure," an invention of Koenig's, is understood the
quotient a formed by the side / of the average growing space of a tree
(considered as a square) and by the diameter of the average stem d.
1
a = —
d
The average distance from tree to tree and the average diameter of a
number of trees is obtained by a number of measurements in the forest.
If the area of the forest is F square feet, then the sectional area of the
forest is
7T F
= — X — square feet
4 a 2
The actual test proves the fallacy of Koenig's assumptions. The ex
planation lies in the fact that the average diameter of a wood is not the
arithmetical mean of the diameters composing it. Further, the growing
space of a tree is not a square.
The actual growing space per tree can be correctly ascertained by laying
a sample strip through the forest, counting at the same time the trees
within the strip. The sectional area of the forest is obtainable, however,
without greater trouble and with much greater accuracy, from the pro
duct calipered sectional area of trees in the sample strip times area of the
forest over area of the sample strip.
On an acre of average soil, there is on an average room for the fol
lowing numbers of healthy trees, according to age :
At 20 years 1,600 specimens.
At 50 years 600 specimens.
At 100 years 240 specimens.
At 150 years 150 specimens.
34
Forest Mensuration
PARAGRAPH LV.
algon's universal volume tables.
Socalled "universal volume tables" have been constructed by H. Algon,
a Frenchman. For a description of these tables see "Indian Forester"
of July, 1902.
The volumes given for each diameter of trees, whatever the species be,
are presented on a number of tables as follows :
Volume in Cubic Feet.
Diameter.
Tabk
: 1. Table 5.
Table 10.
Table 15.
Table 20.
6"
2
3
4
6.
8.
9"
5
8
10
16.
18
12"
9
15
21
27.
33
15"
19
28
39
50.
61
18"
27
39
59
69.
84
21"
43
60
83
109.
128
24"
54
78
108
138.
168
27"
72
107
147
188.
228
30"
87
129
177
228.
276
33"
in
163
221
288.
349
36"
129
189
258
333
405
The tables are used as follows :
1. Caliper the entire forest according to diameters and species.
2. Measure a number of type trees, selected at random, after felling
them.
3. Find that volume table amongst the 20 tables given which best cor
responds with the diameters and volumes of the type trees. Apply the
volume table, which is found to be the proper one, to all diameter classes
calipered in the woods.
Objections to the method are:
a. The danger of mistakes is very great. In an absolutely even aged
wood, one tree of 15 inches diameter may easily show 50% more volume
than another tree of the same diameter, the latter being more tapering
and shorter.
b. In an uneven aged wood the tables are necessarily wrong because
the form height is a function of age as well as of height and diameter.
c. The method does not give any idea of the proportion of logs, fuel,
bark, etc.
Algon calls these tables "universal" assuming that they hold good for
all species of the universe.
Forest Mensuration 35
PARAGRAPH LVI.
schenck's graphic method.
This method, as well, can be used only for sound woods. No calcu
lation is required. The procedure is :
1. Caliper the whole wood.
2. Cut sample or type trees of small, big and average diameters, find
the contents of each tree separately, together with the composition of
contents as logs, fuel and bark.
3. On a piece of cross section paper, use as many units along a hori
zontal line as there are trees (or tens or hundreds of trees) calipered.
4. Mark the unit which each sample tree, according to its diameter,
would occupy if the biggest tree were placed to the right and the smallest
to the left of the horizontal line.
5. Enter over the marked units the volume of the type trees (accord
ing to the composing factors, if required) in square units. A square unit
might correspond with ten feet board measure, or with 1/100 of a cord,
etc.
6. Draw a line joining the ends of the columns, adjusting it by an
average curve.
7. Measure the space (in square units) between the curve and the
horizontal line with the help of a planimeter; the number of square units
giving directly the number of feet Doyle, or of cords, etc.
If there are several assortments of volumes, several curves must be
drawn. This method allows of separating the volumes of trees allotted
to the several diameter classes. Mathematical errors are, practically,
excluded.
PARAGRAPH LVII.
FACTORS GOVERNING THE SELECTION OF A METHOD OF VALUATION SURVEY.
In the case of a valuation survey ("stock taking") in the woods, the
following points must be considered :
a. The degree of exactness required, which depends on the purpose
at stake {c. g., scientific investigations, or preparation for logging, or
taxation).
b. The regularity, uniformity and soundness of the growing stock.
c. The minimum diameter of logs ; assortments ; marketability of spe
cies.
d. The possibility of cutting sample trees.
e. The expense permissible.
The question usually arises whether the entire forest or sample plots
only must be surveyed. The answer depends on the configuration of the
ground, uniformity of the growing stock as to size, age, species and
quality of its components ; further on the value of stumpage, on the accu
racy required, on the available time and on the available funds.
36 Forest Mensuration
The following METHODS OF VALUATION SURVEYS might be
distinguished :
I. Cutting sample trees.
a. Sample trees selected for about five diameter classes, each
class containing about onefifth of the number of trees pres
ent (DraudtUrich method).
b. Sample trees selected for about five diameter classes, each
class containing about onefifth of the sectional area of all
trees present (Robert Hartig method).
c. Sample trees selected as averagediametertrees of the entire
forest (Old Bureau method).
d. Sample trees selected at random — c. g., from dead and down
trees (C. A. S. method — applied in the Balsams; Algon
Universal tables; Graphic method).
e. Stem analysis, together w T ith investigations as to thickness of
bark.
II. Without cutting sample trees.
a. Measuring height and diameter and estimating form figure of
sample trees.
b. Measuring rectified heights and diameters.
c. Measuring merely diameters and estimating form heights.
d. Photographing sample trees, having a scale — say a sti^k 6 feet
long — on the picture.
III. With the help of volume tables.
IV. With the help of yield tables.
PARAGRAPH LVIII.
FACTORS INFLUENCING THE SELECTION OF SAMPLE PLOTS.
If sample plots are taken, there must be determined:
a. The number, situation and distribution of the sample plots.
b. The absolute and relative size of the sample plots. The Bureau of
Forestry prescribes sample plots equalling from I to 4 l A% of the forest.
The "Forest Reserve Manual" prescribes 5% or more.
c. The form of the sample plots and the manner by which the size of
the sample plot is ascertained.
In Europe an ordinary workman calipers, on an average, 5,000 trees
(in maximo 12,000 trees) per day. In Pisgah Forest 500 trees is a good
day's work for one estimator and one helper.
Forest Mensuration 37
• PARAGRAPH LIX.
SIR DIETRICH BRANDIS' METHOD.
The Brandis method is indicated where the object at stake consists in
a rapid survey of the stumpage on large tracts, like the vast Teak and
Bamboo forests of upper Burmah.
Traversing existing trails of known length on horseback, the estimator
records the diameter of each tree within a given distance (say 200 yards)
on either side of the trail.
The widths of the strips traversed multiplied by the length of the trail
yields the area of the sample plot. The number of the trees of the
various diameters found on the sample strip appears from the records.
PARAGRAPH LX.
PIXCHOTGRAVES METHOD ADOPTED ON DR. WEBB'S ESTATE.
1. Sample acres, measuring 4 x 40 poles, are irregularly laid into
swamps, hardwood slopes and spruce slopes. The sum total of the sam
ple acres is 3^% of the total acreage.
2. The length of a sample acre is actually chained off, whilst the width
is ascertained (two poles to the left and two poles to the right of the
chain) by tape, by pacing and by estimating.
3. The sites of the sample acres are not marked on maps.
4. All trees on the sample acres are calipered ; a number of heights
are taken on each sample acre; for each sample acre the average diam
eter, the average height and the number of trees are ascertained.
5. From these averages is deduced, for all sample acres, the average
diameter, the average height and the number of trees. All these data,
of course, must be given for the various species separately.
6. From volume tables previously constructed the volume of the trees
having average height and average diameter is obtained and is multiplied
by the average number of trees.
7. This multiplication yields the volume of the average sample acre.
Objections to this method of valuation survey are:
a. The tree of average diameter has neither average volume nor
average height.
b. The average diameter should be obtained from the fraction "total
sectional area over number of trees." It cannot be obtained
correctly from the fraction "sum total of diameters over num
ber of trees." Similar objections hold good for average height.
c. Guessing at the width of a strip, in dense growth, is rather risky.
38 Forest Mensuration
Remark : Bulletin 36, page 125, states that volumes are now computed
by the Bureau either by averaging the volumes found for the sample
acres, thus obtaining the volume of a model acre as
n
(wherein n equals the number of sample acres) ; or by summing up all
trees of each diameter class, by dividing each sum by the number of sam
ple acres, and by thus finding for a model acre the average number of
trees for each diameter class. In both cases the volumes for each diam
eter class are read from volume tables.
Allowance for defects is made according to local experience, all trees
being calipered as if they were sound.
"* PARAGRAPH LXI.
THE GRIDIRONING METHOD.
i. Work with compass (if a topographical map is required, also with
barometer or clinometer) and with several tapes or ropes. These ropes
are meant to denote the sides of a strip; within the strip the sectional
areas are taken with calipers or Biltmore sticks.
2. The tapes move continuously with the caliper men, and there is
no stopping. The compass man keeps ahead of the measuring crew. One
of the outside "tapers" has the correct length desired for a section. His
tape must be run straight. The inner tapes may make snake linos. The
tally man uses a fresh tally sheet for each section.
3. All strips lie parallel and are equidistant. The width of the strips
depends on the density of growth, smallest diameter calipered, available
help and accuracy required.
4. The distance between two parallel strips depends upon accuracy re
quired, width of strip and variety of configurations.
5. Each strip is divided into sections of equal length. The tally sheet
gives for each section the diameters (with bark) of the trees in that sec
tion ; further, remarks on the run and altitudes of ridges and creeks
traversed, on roads, settlements, existing surveyor's marks, forest fires,
forest pasture, previous lumbering and regeneration. The number of
seedlings in a section might be approximately given under the same head.
Forest Mensuration
39
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40 Forest Mensuration
Advantages of the gridironing method are :
a. A topographical map is obtained at a slight extra expense. The
original survey is controlled and the area of the tract is reascertained.
b. Cruisers are forced to traverse all sorts of country and are not
allowed to skip swamps, cliffs, etc.
c. The proportion of flats, ridges, slopes, swamps, farms, or farm
soil, pastures, etc., is found at the same time.
d. The strips may be used as permanent statistical sample plots, if
they start from definite points (corners) and run in definite directions.
e. The procession of the cruisers is uninterrupted by stops; hence no
loss of time.
For a picture of a convenient tally sheet holder see Graves' Handbook,
page 123.
The gridironing method has been adopted by the working plan division
in a somewhat altered form as follows (Bulletin 36, page 120) :
1. Strips are always one chain (66 feet) wide. A section invariably
comprises one acre equaling 1 x 10 chains.
2. The measuring tape is trailing in the center of a strip ; two caliper
men (proceeding one at the left, the other at the right hand of the tape)
caliper a belt onehalf chain wide, estimating the width at either side
of the central tape.
3. The compass man or tally man with the front end of the tape
attached to his belt goes ahead and stops at the end of every chain,
allowing the calipers to catch up.
4. Thus there are ten stops for every acre; after 10 chains the tally
man enters general notes.
5. Heights may be measured by a separate crew.
A crew of four men calipers in merchantable timber 20 to 40 acres
per day; in small and merchantable timber from 15 to 25 acres per day;
in longleaf pine up to 65 acres per day.
PARAGRAPH LXII.
FOREST RESERVE METHODS.
Roth's Forest Reserve Manual gives three methods of valuation sur
vey, No. 1 and No. 2 being sampleareamethods, and No. 3 an entire
areamethod.
I. Sample circles with a radius of 20 yards, the circle containing
J4 acre ; the radius is estimated, or paced from a central stick. Two
submethods are permitted, namely :
a. Count the number of trees of merchantable size ; estimate the aver
age tree according to log length, taper and thickness of bark; estimate
the percentage of defectiveness (from 10% to 40% after Manual, page 49).
Forest Mensuration 41
b. Caliper the trees in the circle into twoinch classes; estimate the
average tree for each class and allow for defects as before.
In both cases a map must show the site of the sample circles. The
circle method is not allowed in scattering timber. At least 5% of the
entire area must be samplecircled.
2. Sample strips. Strips should be four rods wide, should run across
ridges, should be shown on a map. Otherwise proceed as under 1.
3. The "forty" method is used on surveyed land. It is an entirearea
method applied to 40 acres. The sides of a "forty" are 80 x 80 rods,
equal to 440 x 440 yards. Prescriptions :
ij. Traverse each "forty" on lines about 100 yards apart, thus crossing
4 times.
b. Halt at every 100 yards and estimate the trees within a square of
100 yards surrounding the stopping place.
c. If possible, have a compass man control the length and the direc
tion of your runs.
PARAGRAPH LXIII.
SAMPLE SQUARES.
Sample squares containing about one acre are used in Maine and in
Northern New York. The side of a sample square is 14 rods. A cruiser,
from the center of the square, under the density of the growth existing
in Maine and New York, can overlook a circle of 7 poles radius sur
rounding him. Hence, as a matter of fact — or rather of theory — he skips
the corners of the square, counting only the trees in a circle which has
the side of the square for its diameter. The square contains 196 square
rods, whereas the circle of 7 poles radius contains 155 square rods. The
cruiser estimates the contents of all trees within the "square" from his
central standpoint.
PARAGRAPH LXIV.
PISGAH FOREST METHOD OF 1896.
i. The diameters of all trees promising to yield a log are measured
in diameter classes of ^2 foot interval by a crew of 4 to 5 helpers armed
with Biltmore sticks.
The diameters are measured (or often estimated if beyond reach) at
the point above which the tree is supposed to be sound.
2. Each tree measured is marked by a blaze. The foreman enters on
a tally sheet the species and the diameters called out by the helpers. A
special tally sheet is used for each cove.
3. The average contents of the diameter classes are estimated with the
help of sample trees selected for each species and each diameter — a very
uncertain estimate owing to the unsoundness of the trees.
42
Forest Mensuration
4. Each cove is numbered or lettered to correspond with the tally
sheet on a tree standing at the outlet of the cove.
PARAGRAPH LXV.
PISGAH FOREST METHOD FOR STUMPAGE SALE, BARK SALE AND LUMBERING
OPERATIONS.
i. Each tree is approached individually, its diameter measured and its
defects, especially its hollowness, examined by "sounding." The diam
eter measure and the estimated volume are entered on a tally sheet oppo
site the number of the tree, which is inserted in the stump of the tree
by a stroke of the "revolving numbering hammer."
2. One cruiser and one helper tally 400 trees per day.
3. The method allows of ready control by the owner, the forester and
the buyer. It is adapted to hardwood forests in a rough mountainous
country where the merchantable trees per acre are few; and where no
tree is, practically, free from defects. (Compare Graves' Bulletin No.
36, page 115).
PARAGRAPH LXVI.
HENRY GANNETT'S METHOD, ADOPTED FOR THE TWELFTH CENSUS.
i. Base the estimate on the cruising reports obtainable from the local
lumber companies and railroad companies.
2. Control the applicability of the estimates to huge tracts by .travers
ing them and by overlooking them from a mountain top.
Mr. Gannett expects that mistakes made in one county will be offset
by those made in another.
PARAGRAPH LXVII.
A "FORTY" METHOD USED IN MICHIGAN.
1. A "forty" (a square of 80 x 80 poles) is subdivided into 10 rectan
gles of 4 acres each, measuring 16 x 40 rods.
2. The cruisers estimates when entering a rectangle. He counts the
number of trees on every 4 acres and multiplies the number by the size
of the average tree.
3. For each "forty" the cruiser records in a memorandum the factors
influencing the logging operations or the timber values, notably the
swamps, ridges, forest fires, degree of defectiveness, facilities of trans
portation.
A central line traversing the "forty" in a north and south direction is
sometimes kept by a compassman assisting the cruiser. The outer lines
of the "forty" are plain from the official survey marks.
Forest Mensuration 43
A number of variations of this method exist, according to the custom
of local cruisers and according to the predilections of the lumbermen,
largely governed by the value of stumpage. Compare Graves' Bulletin 36,
page 116.
PARAGRAPH LXVIII.
DR. FERNOW'S "FORTY" METHOD USED AT AXTON.
i. Each "forty" is subdivided into 16 squares of 2^2 acres each, the
sides of a square being 20 x 20 poles.
2. The head estimator, stepping from the corner of the square 10
poles east (or west) and 10 poles north (or south) places himself in
the center of the square.
3. Helpers (students) are sent out, four in number, towards the north
east, northwest, southeast and southwest, each helper reporting the diam
eter and species of the trees found in that onequarter of the 2^ acres
which is allotted to him.
4. The "forties" are carefully surveyed and surrounded by carefully
trimmed lines. The outlines of the 2^2 acre sections are merely paced.
CHAPTER II.— AGE
PARAGRAPH LXIX.
AGE OF TREES CUT DOWN.
The age of trees cut down is found by counting the annual rings on
a cross section (preferably an oblique cut) made as low above the ground
as possible. Allowance must be made for the "stump years," by which
is understood the number of years required by the top bud of the seed
ling, after sprouting, to reach the stump height ("cutting height," after
Circular 445).
Ringcounting in the case of evenporous hardwoods requires the use
of a lens and of some coloring liquid (aniline and ferrochloride) on a
disc planed with a knife, a chisel or a hollow planer.
The difference of the ringnumbers on the stump and the ringnum
bers at any place higher up indicates the number of years used by the
top bud of the tree to traverse the intervening distance. Endogenous
trees do not form any rings.
False rings are formed under the influence of late frost, early frost,
drought, fire and insect pests. They do not run all around the tree.
44 Forest Mensuration
As long as the tree lives, it must annually form a ring of growth (or
rather an additional coat, the sleeves of which cover the branches), the
outside of which becomes a layer of bark, the inside of which is a layer
of wood. In tropical countries this rule does not hold good provided
that there is no change of season.
The formation of rings in the branches is regular. Branchrings are,
however, eccentric and elliptical. The formation of rings in the roots
is said to be irregular, not representing the age of the root, possibly be
cause there is no or little change of seasons in the soil.
PARAGRAPH LXX.
AGE OF STANDING TREES.
The age of standing trees can be estimated only when regular annual
whorls of branches can be counted.
The records of seed years and the history of the forest kept by many
forest administrations usually give an idea of the age of the trees.
PARAGRAPH LXXI.
AGE OF A FOREST.
The age of a forest is the average age of the trees composing it.
In the case of a thicket suppressed for a long time by the superstructure
of a leaf canopy overhead, a socalled "economic age" is frequently sub
stituted for the actual age. In the case of Adirondack spruce, for ex
ample, a diameter of I inch in the center of the trunk had better be
counted, as, say, 15 years, although it may contain as many as 60 rings.
The mean age of an unevenaged wood is defined as follows :
1. That number of years which an evenaged wood would require on
the same soil, in order to produce the same volume as is now at hand.
2. That number of years which an evenaged wood would require in
order to produce at the time of maturity the same volume which the
unevenaged wood is likely to produce.
The latter definition is scientifically more correct. Unless it is adopted, '
an unevenaged wood may get over 20 years older in 20 years, owing
to the fact that the trees dying in the meantime are mostly minors in age.
Forest Mensuration
45
CHAPTER III.— INCREMENT
SECTION I.— INCREMENT OF A TREE.
PARAGRAPH LXXII.
THE KINDS OF INCREMENT.
The following kinds of increment must be distinguished :
a. Increment of height, diameter, sectional area and volume.
b. Current annual increment, current periodic increment and total in
crement.
c. Average annual increment, average periodic increment and average
increment at the age of maturity.
d. Increment of the past and increment of the future.
e. Absolute increment and relative increment.
The increment of stems cut down is found by counting and measuring
the annual rings on several cross sections.
The term "stem" or "tree analysis" designates an investigation into the
past height growth, diameter growth and volume growth of a tree.
Circular 445 of the Bureau of Forestry defines the term "increment,"
somewhat narrowly, as follows : "The volume of wood produced by the
growth in height and diameter of a tree or of a stand."
For definition of the term "tree analysis," see Circular 445 of Bureau
of Forestry.
This circular distinguishes between :
1. Stumpanalysis, being a tree analysis which includes measure
ments of the diameter growth at given periods on the stump
only, no matter what other measurements it may comprise ;
2. Sectionanalysis, being a tree analysis which includes measure
ments of the diameter growth at given periods upon more
than one section of a tree ;
3. Partial tree (stump or section) analysis, wherein the measure
ment of the diameter growth at given periods covers a portion
only of the total diameter growth.
PARAGRAPH LXXIII.
HEIGHT INCREMENT.
The height increment, from the silvicultural standpoint, is of interest
to the forester dealing with mixed woods.
The difference between the number of rings found on two separate cross
sections through the bole indicates the number of years which the tree
4 6
Forest Mensuration
has required to grow through the distance lying between these two sec
tions. By counting the number of rings at several cross sections, one of
which is made as close to the ground as possible, the current and the
average height growth (increment) may be obtained by arithmetical or
by graphical interpolation.
A dense cover favors height increment. In rare instances, however,
the stand of saplings or poles is so close that the height increment of
the individual suffers from lack of food.
PARAGRAPH LXXIV.
THE CURRENT HEIGHT INCREMENT.
In the high forest the current annual height increment reaches a
maximum at an early age; passing this maximum, it sinks more or less
rapidly. The culmination of the current annual height increment occurs
the much earlier and its slackening after said culmination goes on at a
more rapid rate if
i. the species is fast growing and light demanding;
2. the tree observed belongs to the dominant class ;
3. the soil is good.
For yellow pine the culmination of the current annual height incre
ment occurs amongst dominant saplings between the 10th and 15th years;
for spruce at about the 20th year ; for beech and fir between the 25th
and 30th years. Suppressed trees show the maximum of current height
growth much later than dominant trees.
As a general rule for all species, in case of dominant trees, the longest
shoot is made 10 to 15 feet above ground. Slow growing species, shade
bearers and trees stocking on poor soil reach that level at a later date
than trees and species growing under reversed conditions.
In the case of coppice forest, the maximum of the current height
growth lies in the first three years of the life of the shoot. For oak
coppice, the following table may serve as an illustration of height growth :
Growth in Feet.
Age in years
10
20
30
40
5o
Actual height
13'
23'
30'
37'
43'
Current annual increment
1.3'
1.0'
0.7'
0.65'
0.63'
PARAGRAPH LXXV.
THE AVERAGE HEIGHT INCREMENT.
The average annual height increment culminates later than the current
annual height increment, and, after the culmination, it decreases at a less
Forest JMcnsuration 47
rapid rate than the current annual height increment. The average annual
height increment culminates at the very age at which it is equal to the
current annual height increment.
As long as the average increment increases the current increment is
larger than the average. The average increment still rises during a period
of decrease of current increment.
These laws hold good not only for height growth, but also for the
growth of diameter, sectional area and volume. They are based merely
on mathematical principles and are, for that reason, independent of spe
cies, climate and soil.
If "a" denotes the current annual increment, and if "d" denotes the
average annual increment, whilst the indices i, 2, 3, etc. (up to n), indi
cate the year of increment, then the following five equations hold good :
n X d n = aj ( a 2 f a 3 + an
(n 4. 1) d n + 1 = a t f a, + a 3 a u + a n +1
(n + 1) d n + 1 = n X d n + an + 1
n X dn + 1 = n X d u + a n + 1 — d n + 1
n (d n + 1 — dn ) = an + 1 — d n + 1
PARAGRAPH LXXVI.
RELATIVE INCREMENT OF THE HEIGHT.
The percentage of height increment forms, from the start on, an irreg
ularly descending progression.
If the height is h at the beginning of a period of n years of observa
tion and H at the end of that period, then
h X 1. op n equals H
and
n
p equals 100.J— — 100
Pressler substitutes for this formula in case of short periods of observa
tion the following :
200 H — h
n H +h
This formula is derived as follows : Imagine that we are in the midst
of the period of n years. At that time, the increment is apt to be
— ^— , whilst the height at that time is apt to be — : hence, for that mid
n 2
die year, the equation is :
p H — h 2
X
100 n H +h
48 Forest Mensuration
PARAGRAPH LXXVII.
DIAMETER INCREMENT.
The current diameter increment is obtained by counting and measuring
the rings on a disk through the tree. It is generally best to count from
the bark towards the center, along two radii standing perpendicular to
each other.
The general laws of diameter growth are identical with those of height
growth relative to culmination, decrease and increase of absolute (Par
agraph LXXV.) as well as of relative (Paragraph LXXVI.) increment.
If we exclude the buttpiece below chestheight, the annual rings along
the tree bole measured at various elevations above ground show a grad
ual increase of width with elevation, provided that the leaf canopy of
the forest is complete and uninterrupted — e. g., the width of the ring 50
feet from the ground, formed in 1903, is greater than the width of the
ring formed 20 feet above ground in the same year.
For trees standing in open crowndensity, the width of the ring de
creases with the elevation above the ground, especially within the crown
itself.
A tree standing in a thin crowndensity may show an even width of
ring all over the tree bole.
For very old trees in closed stand it is sometimes found that the diam
eter, say 40 feet above ground, is larger than the diameter, say, 20 feet
above ground.
The rings on a disk are not actually circles ; they more closely ap
proach the form of eccentric ellipses (see Paragraph XIII.).
»
PARAGRAPH LXXVIII. *
SECTIONAL AREA INCREMENT.
The increment of the sectional area is obtained from the increment of
the diameters. Where greater exactness is required, and especially in
case of irregular rings, the planimeter or the weight of a piece of paper
having the form of the sectional area may be used for measuring to good
advantage (Paragraph XIII.).
The increment of the sectional area at chest height depends on the
crown density overhead; further, on the quality of the soil. At chest
height the culmination of the current annual sectional area increment
takes place, in the case of dominant trees, fast growing species and com
plete cover overhead, between the years 40 and 70.
The culmination of the current annual sectional area increment occurs
always later than the culmination of the current height and diameter in
crement. After culmination it remains uniform for a long time.
The absolute increment of a sectional area higher up on the bole, com
pared with the absolute increment at chest height, is found to be equal
to it in the case of dominant trees ; larger in the case of suppressed trees ;
and smaller in the case of isolated trees.
Forest Mensuration 49
Pressler establishes as the "law of bole formation" the following rule :
"The absolute increment of the sectional area at any point of a bole is
directly proportioned to the leaf surface above that point."
This rule is, on the whole, correct. An unexpected swelling, however,
is often found at 9/16 of the height of the tree. Within the crown of
the tree, the decrease of sectional area increment is rapid.
PARAGRAPH LXXIX.
RELATIVE INCREMENT OF DIAMETER AND OF SECTIONAL AREA.
The increment percentage at any point of the bole, like all increment
percentages, forms a constantly but irregularly descending progression.
At any point of the bole the increment percentage of the sectional area
is the double of the increment percentage of the diameter.
Schneider gives a handy formula for the sectional area increment per
centage, viz. :
400
P equals
H nd
wherein d represents the diameter at the beginning of the period of ob
servation, and wherein n indicates the number of rings per inch at the
time of observation.
The percentage of the sectional area increment increase along the bole
with increasing height of the disk measured, excepting, however, possibly,
the case of very isolated trees.
The average sectional area increment percentage of the bole is found at
a point a little below onehalf of the total height, namely, at about 0.45
of the total height from ground.
PARAGRAPH LXXX.
VOLUME INCREMENT.
The (current and future) volume increment of standing trees is of
great interest to forest financiers ; it can be estimated only, and cannot
be measured exactly.
The volume increment of trees cut down may be ascertained as follows :
1. By the sectional method, or by "section analysis" (Paragraph
LXXXL).
2. From the increment of sectional area chest high, height increment
and form figures (Paragraph LXXXIV.).
3. From the increment of sectional area in the midst of bole (Para
graph LXXXV.).
4. On the basis of the average annual increment (Paragraph
LXXXVIL, last 4 lines).
5
V
50
Forest Mensuration
PARAGRAPH LXXXI.
SECTION ANALYSIS.
The\sectionmethod is a complete tree analysis by sections. The entire
bole is divided into a number of sections, preferably of even length, at
both ends, or, better, in the midst of which the periodical increment of
the sectional area is ascertained (compare Paragraph XL).
In the latter case, multiplying such sectional areas (in square feet)
as belong to the same age of the tree by the length (in feet) of the sec
tions, the volumes (in cubic feet) of the different sections at given ages
are obtained.
The "top pieces," however, must be figured out separately, their length
differing from the even length of the sections. These top pieces are
usually considered as cones, and their volumes are ascertained as onethird
height times basal area of top piece. The basal area of the top piece is
identical with the upper area of the uppermost full section of a given age.
Example for HuberSections Ten Feet Long.
Total height
25 feet.
40 feet.
67 feet.
Total age
20 years.
40 years.
60 years.
Sectional area of Section i
0.34 sq. ft.
0.78 sq. ft.
1.23 sq. ft.
Sectional area of Section 2
0.15 sq. ft.
0.45 sq. ft.
0.87 sq. ft.
Sectional area of Section 3
0.25 sq. ft.
0. 64 sq. ft.
Sectional area of Section 4
0.03 sq. ft.
0.53 sq. ft.
Sectional area of Section 5
0.25 sq. ft.
Sectional area of Section 6
0.04 sq. ft.
Summary of sectional areas
0.49 sq. ft.
1.5 1 sq. ft.
3.56 sq. ft.
Summary sectional areas x 10
4.90 cu. ft.
15.10 cu. ft.
35.60 cu. ft.
Volume of top piece
0.05 cu. ft.
0.09 cu. ft.
08 cu ft
Total volume
4.95 cu. ft.
15.19 cu. ft.
35.68 cu. ft.
The volume of the top pieces forms in the older age columns an insig
nificant part of the total volume.
If the logs as cut in the woods are used as sections, then each section
has a separate length and its volume must be separately ascertained for
every decade of age of tree.
Remark : It is wise to first ascertain the full age of the tree, allowing
for stump years. It is further wise to throw off that number of years
which exceeds full decades — e. g., in case of a tree 117 years old, 7 years.
Forest Mensuration 51
At the stump the rings had best be counted from the inside out, allowing
for stump years. Instance: Age of tree, 117; stump years, 4 years; count
ing on the stump, from the inside, 6 rings establishes the ring formed in
the year 10. Continuing, the rings of the years 20, 30, 40, 50, etc., up
to year no, are pencil marked. The outside seven rings are thrown off.
At all other disksections, count and measure from the outside in, after
discarding the 7 years exceeding full decades of tree life.
PARAGRAPH LXXXII.
noerdlinger's paper weight method.
The total length of the tree is divided into 8 Huber sections, and cuts
are made in the midst of these sections, at the height of 1/16, 3/16, 5/16,
7/16 and up to 15/16 of the bole. On each cross section the radii are
measured, not with the rule, but with dividers.
On a piece of paper folded 4 times and thus divided into 8 sectors the
measurements are entered with the help of the dividers, one sector being
allotted to the first cross section, the next sector to the next cross sec
tion, etc. Multiplying the total weight of the zone indicating, say, the
year 70, by height of the tree and dividing the product by the weight of
a square foot of paper, the volume of the tree when 70 years old is
directly obtained in cubic feet. Similarly the zones corresponding with
the year 50, 60, etc., are cut out, weighed and multiplied.
If the volume increment percentage p alone is to be obtained, then it
is enough to divide, say, the "weight" of the year 70 by the weight of
the year 60, and the 10th root of the quotient will equal i.op.
PARAGRAPH LXXXIII.
schenck's graphic tree analysis.
Graphic tree analysis offers the following advantages :
1. Mistakes are impossible, being at once noticeable on the diagram
paper.
2. The volume in feet Doyle can be readily obtained for any stated
minimum diameter.
3. The graphical sketch is adaptable to any of the 43 scales in use in
the United States, as well as to the metric system.
4. The thickness of heart wood and sap wood and bark readily appears.
5. It is immaterial whether measurements are taken in meters or in
feet, the graphical sketch readily allowing of transfers into other units.
6. Height growth and diameter growth appear at the same time, and
from the same entries.
7. The length of the sections taken need not be uniform.
The method of proceeding is as follows : On millimeter paper a system
of coordinates is established; heights are entered as ordinates, diameters
52
Forest Mensuration
or radii as abscissas. The scale for the height entries should be much
smaller than that of the diameter entries.
Diameter points, at the different sectionheights, corresponding to a
given decade of years are joined (beginning at the outside), by which
procedure the outline of the tree at that decade is established.
Th top cones are obtained by prolonging such outlines arbitrarily until
they intersect with the heightaxis.
The merchantable bole for each decade is dissected, on the diagram,
into logs the length and diameter of which are measured on the diagram.
PARAGRAPH LXXXIV.
wagener's method and stump analysis.
Wagener recommends a partial stem analysis for cases in which a
knowledge of the absolute increment, not a knowledge of the absolute
tree volume, is required. Tree volume is sectional area chest high times
height of tree times form factor.
Wagener analyses :
a. the height growth by counting the rings at various altitudes along
the bole ;
b. the growth of the sectional area at chest height by measurement in
decades in the usual way.
Wagener then estimates the form factor according to form factor tables.
In the latter proposition, obviously, lies the danger of mistakes. Since,
however, increment is a difference of volumes, merely the difference of
mistakes — a comparatively small item — enters into the problem. ►
Age in years
60
80
100
120
14
17
19
21 .
Sectional area b. h
0. 25
0.35
0.50
0.71
Height in feet
75
85
93
105.
Form factor
0.50
0.50
0.50
050
Volume in cubic feet
94
13
23
36.
3
5 ic
). 1
3
The "stump analysis" (compare Paragraph LXXII.) introduced by
the Bureau of Forestry rests on premises similar to those proffered by
Wagener.
If the form height for the stumpdiameters (or the number of feet
b. m. per square foot of stump area for given stump diameters) is known,
the rate of volume increment can be quickly ascertained by mere stump
analysis.
Forest Mensuration 53
It is, however, a well known fact that the diameter growth at the
stump — especially at a low stump — is particularly unreliable as an index
of volume growth, owing to the exaggerating influence on stump growth
exercised by light, by water, by depth of soil and by superficial roots.
Stump analysis as a means to bring a volume in reference to a sec
tional area at the stump is permissible only as a necessary evil.
PARAGRAPH LXXXV.
pressler's method.
Frequently the task before the forester is merely that of ascertaining
the increase of bole volume during the last 10 or 20 years. Then after
Pressler, one single investigation into the growth of the sectional area is
sufficient when made with the help of the accretion borer in the midst of
the "decapitated" bole. The volume increment in cubic feet equals the
sectional area increment in question multiplied by the height of the
tree.
The bole is decapitated by that number of top shoots which have been
formed during the period of observation. This operation corresponds
very well with the usual practice of judging the bole increment per
centage from the sectional area increment ascertained at 0.45 of height
of tree.
Pressler measures the sectional area at the end of the period of observa
tion too large, measuring it at too low a point. He multiplies this sec
tional area, however, by too small a height — namely, the decapitated
height; thus a mistake made in the positive sense is apt to be eliminated
by a mistake made in the negative sense.
The axe can be used to better advantage frequently than the accretion
borer.
PARAGRAPH LXXXVI.
breymann's method.
Breymann gives the following formula : ' Kic^
1. For the current annual volume increment T: ^ "^.^,
T = V ( 3 d + T) <~*^^^^~i )
wherein "8" and "A," denote the annual increase of diameter "d" and
length ''1" respectively.
2. For the corresponding increment percentage P:
8 X
P = 100(2 +T )
It appears that for trees of old age and hence of little height growth
the increment percentage is merely dependent on the diameter increase.
54
Forest Mensuration
Breymann, however, neglects :
1. The change of form figure, during the period of observation;
2. A number of small factors which ought to be embraced in the
formula.
For stopping height growth or for A, = , the term given for P can
be easily reduced to the term given by Schneider for the sectional area
increment percentage.
'
■ ~ ^ PARAGRAPH LXXXVII.
FACTORS INFLUENCING THE CUBIC VOLUME INCREMENT.
*M*
■
A.
The culmination of the current annual volume increment takes place at
a later year than the culmination of the sectional area increment at breast
■ • height. Naturally so, because with increasing age of a tree, its root sys
tem as well as the branch system, the feeders of the body, show contin
uous increase.
Big and long branches, of course, require a great deal of wood fibre
to increase and maintain their own strength, like levers increased in
length. Hence, from a certain size of branch on, all wood fibre produced
by the branch is used up within the branch itself, for its own purposes,
instead of being added as increment to the merchantable bole.
After Dr. Metzger, the crown of a tree yields the maximum of bole
increment if its crown diameter is, and if the number of trees per acr<*
are:
Quality of soil.
Diameter of crown, in feet.
No. of trees per acre.
Very good.
16.5
203
Good
147
256
Medium
12.7
343
Poor
93
640
Very poor
8.3
807
From the theoretical standpoint it seems wise, consequently, to force
the lower branches of a tree to die, with the help of proper tension and
friction within the leaf canopy, when they exceed a length of 8.25, 7.35,
6.35, 4.65 and 4.15 feet respectively (the halves of the diameters).
Metzger's investigations are interesting, but his conclusions seem to be
too sweeping.
P. P. Pelton recommends the lopping of branches in order to shorten
the length of the branchlevers.
The average annual volume increment of dominant and sound trees
Forest Mensuration
55
culminates at a very high age only, if ever, owing to the late culmina
tion of the current annual average increment.
The volume increment percentage forms — as in all cases of increment —
a steadily but irregularly decreasing progression. This percentage is in
variably equal to or higher than the sectional area increment percentage
at chest height.
Roughly speaking, the volume increment percentage amounts to from
i to 1.7s times the sectional area (at chest height) increment percentage,
or, as Pressler gives it, to from 2 to 3^2 times the diameter (at chest
height) increment percentage.
Crown;'covers part of bole
■>.
£ or more.
itot
Less than \.
Wo
>X * Height Growth.
Seemingly nil.
2.67
Medium.
2 . 67  < •>
Good
v G °*
.3.00 .«
133UC
Excellent.
W t>ti ■■> ■> ■ < *  >
3i7U*^
3331,1* V*
#\
■V
Since the average volume increment of a tree is equal or closely equal
to the current annual increment at a high age only, it is usually not
permissible to substitute the average increment, which is easily ascer
tained, for the current annual increment.
PARAGRAPH LXXXVIII.
VOLUMEINCREMENT PERCENTAGE OF STANDING TREES.
In the case of standing trees the volume increment percentage cannot
be measured, owing to the impossibility of ascertaining a change of form
height.
The Pressler data given in the preceding paragraph allow of estimating
the volume increment percentage of standing trees on the basis of a
diameterincrease, measured at breast height.
The Pressler "accretion borer" is used for the purpose, or an axe.
Stoetzer, Director of the Forest Academy at Eisenach, modifies the
Schneider formula for sectional area percentage, writing it
C
P = n¥
wherein n indicates number of years (rings) required to form one inch;
d represents the diameter at the beginning of the period of investigation,
whilst C (the socalled "constant factor of increment," which is not a
constant factor at all) must be ascertained for a given species, soil, diam
eter, age and position by actual tests on felled trees.
In old dense beech woods C is, e. g., 540. After a seed cutting in the
same woods during the final stage of regeneration C is only 450 (observa
tion by Dr. Wimmenauer).
56 Forest Mensuration
Trees growing as cones would grow, have C equal to 600; trees grow
ing as Apollonian paraboloids would grow, have C equal to 800; after
Stoetzer, C might amount to as much as 930, in case of suppressed trees.
The minimum possible (in sound trees) for C is 400.
The Pressler values given in the table of the preceding paragraph
closely correspond with the constant factors of increment ascertained
after Stoetzer. In the case of the Pressler table (at end of Paragraph
LXXXVII.) we find, for medium height growth and very small crown,
a factor 3.00 by which the diameter increment percentage is to be multi
plied. This factor 3.00 corresponds with 600 for a constant factor of in
crement.
If the diameter in the midst of the bole is l / 2 of the diameter at the
end, then the tree, it seems, is conical, and an increment factor of 600
might be assumed. If the sectional area in the midst of the bole equals
y 2 the sectional area at the end, then the tree is a paraboloid, and the
increment factor seems apt to be 800.
It must be remembered, however, that a tree forming a paraboloid
grows as a paraboloid only, if its percentage of height growth is equal to
its percentage of growth of sectional area — a rare case in merchantable
trees.
Similarly, a tree growing as a cone must have the height increment
percentage equal to its diameter increment percentage.
If n and v represent the number of rings per inch added to original
diameters d and 8 at chest height and at 0.45 of the height of the tree
respectively, then the "constant factor of increment C" is found as follows :
400 C
p (volume)
v8 nd
nd
C = 400
PARAGRAPH LXXXIX.
INTERDEPENDENCE BETWEEN CUBIC INCREMENT AND INCREMENT
IN FEET B. M. DOYLE.
Doyle's rule underestimates the contents of small logs and overesti
mates those of big logs.
Consequently, the growth of a tree bole in feet b. m. Doyle is (for
small trees yielding logs under 28" diameter) relatively faster than the
growth of a tree bole expressed in cubic feet. The figures of Column D
denote, in the following table, this excess rate of growth :
Forest Mensuration
57
A
5
C
D
No. of ft. b. m. per
Differences of con
"Extraordinary"
Diameter of logs
one eu. ft. of tim
secutive figures in
percentage of incre
without bark.
ber estimated
Column B.
ment Doyle coin
after Doyle.
ciding with
1" growth.
12"
509
0.41
S.i
13"
5 SO
o.35
6.4
14"
535
033
57
15"
6.18
0.26
4.2
16"
6.44
0.27
43
17"
6.71
0.22
33
18"
693
0. 14
2. 1
19"
7.07
0.26
32
20"
733
0.18
25
21"
751
0. 16
2.2
22"
7.67
0.15
2.0
23"
7.82
0.13
i7
24"
795
0. 14
1.8
25"
8.09
0. 11
i4
26"
S.20
0.12
15
27"
833
0.09
1 . 1
28"
8.41
0. 11
1 . 1
29"
8.52
0.08
1 .0
30"
8.60
...
For the standard rules, the increment percentage of a tree can be ascer
tained by cubic measure as well as by standard measure.
If n years are required to form one additional inch of diameter, then
the extraordinary percentage of Doyleincrements amounts annually to
yl.OD, wherein D represents the values of Column D in the foregoing
table.
By this factor j/l.OD, the cubic volume increment percentage of a
bole may be converted, ceteris paribus, into Doyle increment percentage,
provided that
58 Forest Mensuration
i. The cubic increment percentage of the total bole coincides with the
cubic increment percentage of the merchantable bole ;
2. The merchantable bole does not increase in length during the period
of observation.
PARAGRAPH XC.
CONSTRUCTION OF VOLUME TABLES.
Volume tables are "tree yield tables" from which the volume of a tree
of given species, given age, given diameter breast high or stump high,
given height, given merchantable bole, given position (suppressed, dom
inant, etc., or isolated, crowded, etc.), given locality and so on can be
readily read. The units of volume are cubic feet, board feet, standards,
cords, etc., according to the requirements of the case.
Obviously, volume tables give, or should give, the volumes of average
trees ; they may give, in addition, the maximum and minimum volume
possible in a tree of stated description.
Volume tables are constructed either on the basis of hundreds (thou
sands) of measurements taken from trees actually felled in the woods
(possibly also sawn at a saw mill, to ascertain the grades) or on the
basis of a smaller number of complete section analyses.
The rapidity of volume growth of a species and the development of its
form height depend on many local factors — notably on climate, soil, sylvi
cultural systems at hand, influence of fires, fungi, insects, etc.
Owing to the multitude of local factors influencing the volumes and
the changes of volumes, local volume tables alone are entitled to & place
in exact mensuration.
Volume tables for second growth are more reliable than volume tables
for first growth.
Circular 445 of Bureau of Forestry defines volume table as "a tabular
statement of the volume of trees in board feet or other units upon the
basis of their diameter breast high, their diameter breast high and height,
their age, or their age and height."
The method of construction of volume tables is either mathematical or
graphical.
1. Mathematical method.
The volumes ascertained for trees of a given diameter (breast high or
stump high with or without bark), a given merchantable length or total
length, a given age or a given quality or locality are added up.
The sum total of these volumes divided by the number of trees forming
it yields the average volume of the tree of stated description.
These averages are shown, for the various diameters, lengths, ages and
localities, in tabular form.
The volumes corresponding with such diameters, lengths, ages and lo
calities, for which sample trees were not cut and measured, are found by
arithmetic interpolation.
Forest Mensuration 59
Finally, the differences in volume shown by average trees of similar
description (1. e., differing but slightly in diameter, length, etc.) are
formed and rounded off in a manner causing the volumes to show a more
steady mathematic progression.
2. Graphic method.
The volume of each tree measured is entered as the abscissa on a
diagramsystem of coordinates, whilst the diameters of the trees (or the
age, etc.) are registered on the ordinate axis. Similarity of length is in
dicated by color of mark representing the tree; similarity of locality is
indicated by the form of the mark (square, triangle, cross, circle, etc.).
Corresponding marks are then joined by chains (having square, cir
cular, triangular links) of the proper color.
Finally, average curves as well as maximum and minimum curves
are drawn for the various colors and forms of marks.
Maximum and minimum curves should not represent the very best
and the very worst possibilities ; they should represent the average of
very good and very bad trees.
The graphic method is more reliable, because less depending on mere
figures, than the mathematical method. Both methods are frequently
combined.
A number of complete tree analyses furnishes more reliable results than
a large number of mere volume measurements because it yields more
reliable curves (guidecurves) of development for one and the same lo
cality, and because it prevents the forester from drawing curves of growth
at random.
If the sample trees (or sample logs) are sawn up at a saw mill where
the lumber is properly graded according to the inspection rules prevailing
for the species in question, the volume tables may also give the actual
average output of specified trees in lumber of the various grades.
SECTION II.— INCREMENT OF A WOOD.
PARAGRAPH XCI.
INCREMENT OF FORESTS.
The volume increment of the virgin forest is on the whole nill.
In America the value increment of a primeval forest is based more on
a price increment of stumpage than on a volume increment of trees. The
volume increment, in addition, can scarcely be ascertained with sufficient
accuracy for a given piece of forest at a reasonable expense.
In second growth forests, on the other hand, say in Virginia, an abso
lute knowledge of the productiveness of the forest renders forestal invest
ments safer in the eyes of the owner ; and the safety of the investment it is
which alone can tempt the capitalist to invest in forestry. A knowledge of
60 Forest Mensuration
the increment in second growth woodlands can be obtained from tabulated
statements ("yield tables") showing the rate of growth for woodlands of
a given species in a given locality. Under normal yield tables are under
stood such tables which give the rate of growth for eveneged, pure, nor
mally stocked, well thinned woodlots for given localities (compare Para
graph LIII. and XCIV..).
Such normal yield tables are constructed abroad for beech, pine, spruce,
fir and oak. In this country they exist only in Pinchot's and Graves'
yield tables for white pine. In America, pure evenaged woods are found
in rare cases only (taeda, echinata, rigida, jack and longleaf pines, tama
rack, coppicewood).
In the construction of normal yield tables the following points require
consideration :
i. The different methods of construction (Paragraph XCIL).
2. The combination, interpolation, adjustment and correction of the
results (Paragraph XCIIL).
3. The contents and use of yield tables (Paragraph XCIV.).
PARAGRAPH XCIL
METHODS OF CONSTRUCTION OF NORMAL YIELD TABLES.
Normal yield tables may be based on :
A. Repeated survey of some typical woodlots during their entire life
time. »
B. Repeated survey of different woods standing on an equal quality
of soil, during a period of years equal at least to the longest difference in
age found amongst them.
C. Onetime, simultaneous survey of a very large number of woods of
different ages standing on different qualities of soil. Missing links are
here obtained by graphic or mathematical interpolation (Paragraph
XCIIL).
If tables are constructed by repeated survey of several woods (B), it
is often found that the links cross one another for unexplainable reasons.
PARAGRAPH XCIIL
GATHERING DATA FOR NORMAL YIELD TABLES.
In order to see whether or not two woods, in the case C of the pre
ceding paragraph, belong to the same chain of growth, two methods are
in use :
a. The horn or curve method, after Baur.
b. The stem analysis method.
Forest Mensuration 61
Remarks on a:
The contents and age of all woods (normal) surveyed are plotted in a
diagram, the age forming the abscissa and the volume the ordinate of the
system.
Curves are then drawn outlining the maxima and minima of growth
observed.
The hornshaped space between these curves is divided into a number
of sectors equal to the number of yield classes to be distinguished. The
middle line of each sector illustrates the productiveness of its class.
The average height growth is obtained in a similar way, the height data
forming the ordinates in a system of coordinates.
Baur finds that the allotment of a given plot to a volumesector corre
sponds with its allotment to a height sector. In other words, the height
is, after Baur, an absolutely reliable indicator of the quality of the soil,
or, what is the same, of the yield class.
The growth of sectional area, height and volume being known, the
development of the form factors for the various sectors is readily ob
tained from the fraction
sXh
Remarks on b:
An analysis of the average stems in lots surveyed would not throw
any light on their connection as members of one and the same chain
of observation. After Robert Hartig, the 200 strongest trees are analyzed.
After Wagener, the ideal cylinders merely of these 200 strongest stems
are analyzed by ascertaining their height growth and their diameter
growth at breast height. Weise and Schwappach are satisfied with an
analysis of the heights merely of the 200 best stems.
The selection of sample plots is not easy, even in second growth raised
under forestal care. A valuation survey establishes for each plot the
number of stems and the sectional area for each diameter class of stems
(usually divided into 5 classes) ; further, the average age and the average
height of the plot. The volume is then figured out, usually, according
to the DraudtUrich method.
The experiment stations maintained by the European Governments
control the growth of a large number of experimental plots, which should
not be smaller than y 2 acre each.
The sample plots are corner marked, and, more recently, the individual
trees contained therein are numbered consecutively. Surveys of these
plots are made every five years. The point of measurement is indicated by
a chalk line.
In America normal sample plots have not been established as yet by
the Bureau of Forestry in second growth. The sample plots at Biltmore
do not represent a normal second growth.
62 Forest Mensuration
PARAGRAPH XCIV.
NORMAL YIELD TABLES, THEIR PURPOSES AND CONTENTS ABROAD.
Normal yield tables are especially used for the following purposes:
i. To ascertain the quality of the soil (c. g., for taxation).
2. To ascertain the volume of the growing stock.
3. To ascertain future yields of the forest.
4. To solve problems of forest finance, especially those of forest ma
turity (length of rotation).
German normal yield tables have the following contents :
A. Tables for the main forest — the secondary forest comprising such
trees on the same lot as are about to be removed by way of thin
ning :
(1) Age, graded at five year intervals.
(2) Number of trees.
(3) Sectional area at chest height, inclusive of bark.
(4) Average diameter.
(5) Average height and height increment.
(6) Volume in cubic measure arranged according to assortments
as logs, fuel, bark, etc.
(7) Periodical and average annual volume increment.
(8) Increment percentage.
(9) Form factor.
(10) Normal growing stock.
B. Tables for the secondary forest, giving merely its vol ume,» which,
as stated, is to be removed by way of thinning.
Circular 445 of the Bureau of Forestry defines "future yield tables" as
follows : "A tabular statement of the amount of wood which, after a
given period, will be contained in given trees upon a given area expressed
in board feet or some other unit."
PARAGRAPH XCV. **«■*« STVm »r \» * «*
RETROSPECTIVE YIELD TABLES.
In "retrospective" yield tables an attempt is made to rebuild the grow
ing stock as it was before lumbering from the stumps found on the
ground and from stem analyses of the trees now standing. Prerequisite
is a knowledge of the year in which lumbering took place and of the
conditions of growth since prevailing.
Method of proceeding:
1. Make stem analyses and construct tree volume tables, showing the
probable contents of trees for stumps of a given diameter and for given
diameters b. h.
Forest Mensuration 63
2. On land cut over n years ago, find by valuation survey and stem
analyses :
a. The present volume "F."
b. The volume "y" of the trees now standing as it was "n" years ago
with the help of tree volume tables.
c. From the stumps the volume "x" of the trees logged "n" years ago.
3. A product of "F" units (with an undergrowth not fit for logging)
has been derived in "n" years from an original stand aggregating "y"
plus "x" units of volume.
4. Grouping hundreds of sample plots together, yield tables for local
use are obtained. Misleading is, of course, the multiplicity of conditions
(mixture of species, soils, original stands, pasture and fire) surrounding
a second growth which check the applicability and the combination of
the tables found.
The tables are way signs, not ways, toward a true knowledge of the
productiveness of cutover woodlands.
PARAGRAPH XCVI.
YIELD TABLES OF THE BUREAU OF FORESTRY.
Bureau yield tables are meant to show the growth on cutover land
occurring within the next 10, 20 or 30 years, if a tract is logged to a
10", 12" or 14" (or any other) limit. Bureau yield tables are based on
tree volume tables and on an account of the numbers of tree individuals
found in the various age classes of forest, viz., diameter classes of trees.
The influence of the different qualities of soil on tree growth is not
given, only one average volume table being constructed. The volume
tables show the number of years which a tree requires to increase its
diameter b. h. by one inch. The volume tables record, in addition, the
volume increase corresponding with such diameter increase. Applying
these findings to the stumpage presumably left after logging, the volume
can be ascertained which is expected to be on hand 10, 20 or 30 years
later. The volume growth is forecasted, as if it were taking place under
primeval conditions.
The Bureau neglects entirely the death rate of trees, due to natural
causes and especially high amongst seedlings and saplings, or else due
to the logging operations themselves. The results forecasted in this way
must be invariably too high.
Pinchot's Spruce Tables (The Adirondack Spruce, p. 77) are based on
similar premises :
a. Construct volume tables by stem analysis (stumpanalysis) on land
cut over for a second time, thus showing rate of growth for trees left
standing at the first cut.
b. Construct tables, by actual measurements in the woods, giving the
6 4
Forest Mensuration
number of trees of the various diameters, composing a stumpage of from
1,000 to 12,000 feet board measure.
c. Predict the number of trees and their exact diameters to be found
10, 20 or 30 years after logging, according to severity of logging (diam
eter limit).
d. With the help of the volume tables, give the contents of these trees.
In these tables as well, the death rate amongst trees is disregarded. For
normal death rate, compare Pinchot's "White Pine," p. 80, ff; also remarks
at end of Paragraph LIV.
PARAGRAPH XCVII.
THE INCREMENT OF A W00DL0T.
The current as well as the annual average increment of normal, even
aged woods culminates at a much earlier date than the increment of the
trees composing such woods. The explanation lies in the death rate of
the trees.
Under a close crown density in evenaged, normal woods, the stronger
half of the trees yield, from the pole stage on, practically all the incre
ment, the weaker half of the trees being almost inactive.
The better the quality of the soil, the earlier occurs the culmination of
the increment; consequently, on good soil, shorter rotations are apt to be
advisable than on poor soil.
Light demanding (intolerant) species show an earlier culmination than
shade bearers (tolerant) species.
For white pine woods, after Pinchot, the years of increment culmina
tion are as follows :
Culmination
For entire volume with
bark in cu. ft.
For volume Doyle in
ft. b. m.
of
I.
II.
III.
I.
II.
III.
Current inert.. . .
Average inert . . .
40th
60th
50th
80th
60th yr.
1 ooth yr.
70th
i35th
70th
1 60th
noth yr.
210th yr.
I denotes best; II denotes medium, and III denotes poorest quality of
soil.
The increment of a woodlot, whether normal or abnormal, can be
obtained :
a. With the help of yield tables.
b. By special investigations made into the rate of growth of sample
trees (Paragraph XCVIII.).
Forest Mensuration 65
c. With the help of the average annual increment of the woodlot (Par
agraph XCIX.)
The increment of a past period is never exactly equal to that of a
future period, unless the age of the woods is close to that year at which
the increment culminates. The increment percentage during a past period
is always larger than the increment percentage during a coming period
(aside of temporary increase due to lightincrement).
The general laws (Paragraph LXXV.) relative to the culmination,
increase and decrease of increment hold good for the volume increment
of woodlots as well as for that of trees.
PARAGRAPH XCVIII.
ASCERTAINING THE INCREMENT OF WOODLOTS BY SAMPLE TREES.
The current annual volume increment and the volume increment per
centage of a wood, from which its maturity largely depends, can be cor
rectly found only by a valuation survey, combined with an investigation
into the present rate of growth exhibited by a number of sample trees.
Borggreve recommends to gauge the increment of the sample trees by
the Schneider increment percentage. This is usually insufficient.
The correct volume increment percentage p of a woodlot is obtained
from the volume increment percentage pi, pn, p3, p< and ps of the class sam
ple trees — which represent classvolumes vi, vj, vs, V4 and x — as
v i Pi + v j P 2 4 v 3 p 3 + v 4 p 4 + v 5 p 5
V l + V 2 4" V 3 + V 4 + V 5
Where the form heights of the classes differ slightly only, the sectional
areas of the classes may be substituted for the volumes of the classes.
Again, where classes of equal sectional area are formed (after Robert
Hartig), there the volume increment per cent, of the woodlot equals the
arithmetic mean of the volume increment percentages of the sample
trees, so that
Pi +P2 + Ps + P4 + P5
PARAGRAPH XCIX.
CURRENT INCREMENT ASCERTAINED FROM AVERAGE INCREMENT.
Within certain limits, a short time previous and a short time after the
culmination of the average annual increment, the annual average incre
ment equals the current increment and can be used in its place as a basis
for yield calculation. European Governments frequently prescribe this
modus operandi for yield forecasts in working plans.
66 Forest Mensuration
CHAPTER IV.— LUMBER
PARAGRAPH C.
UNITS OF LUMBER MEASUREMENT.
For rough lumber one inch thick, or thicker, the unit of measure, known
as one foot board measure, is a square foot of lumber one inch thick.
*" v ^~""* (,"i^)This unit is the i/i2th part of a cubic foot.
■ For rough lumber thinner than one inch, the unit of measure, also
, $ known as one foot board measure, is the superficial square foot, and the
thickness of the lumber is here entirely disregarded.
All dressed stock is measured and described as if it were the full size
of the rough lumber necessarily used in its manufacture. "Inch flooring,"
e. g., is actually 13/16 inch thick ; and "^ inch ceiling" is actually 5/16
inch thick.
Standard thicknesses are:
tff » J • h ' 8 ' *' J > I i' x 2' 2 ' 2 2> 3 x 4 •
Standard lengths are:
in hardwoods 6 to 16 feet;
in softwoods 10 to 24 feet.
In both cases, lengths in even feet (not in odd feet) are required.
A shortness of 1" or 2" in the length of hardwood boards is disregarded.
Standard defects are :
I. In hardwoods: one sound knot of 1 \" diameter;
one inch of bright sap ; ►
one split, its length in inches equalling the contents of
the board in feet b.m.
II. In softwoods : sound knots, viz. :
(a) pinknots of not over J" diameter;
(b) standard knots of not over ij" diameter ;
(c) large knots of over i\" diameter;
pitchpockets, viz. :
(a) small pitchpockets J" wide;
(b) standard pitchpockets up to " wide and up to 3'
long;
pitchstreaks, viz. :
(a) small pitchstreaks not wider than j l 5 the width and
not longer than }■ the length of board ;
(b) standard pitchstreaks with dimensions up to twice
as large as given under (a);
sap, viz..:
(a) bright sap ;
(b) blued sap ;
splits, wane, scant width, tongues, less than y\" long.
Forest Mensuration 67
The point at which a defect is located greatly influences its effect on
the grade of the lumber.
The two faces, the two edges and the two ends of a board must be
parallel. In case of unevenness, the thinnest thickness, the narrowest
width and the shortest length are measured.
Lumber is measured with the help of a lumber rule (Lufkin rule) which
yields for inch boards of given lengths and given width the correspond
ing contents in feet b. m.
In measuring the widths, fractions of an inch are neglected in rough
lumber.
PARAGRAPH CI.
INSPECTION RULES AND NOMENCLATURE.
The lumber inspection prevailing in a given market is governed by
local custom or by agreement within the body of local associations of
lumbermen.
The tendency of all inspection rules is directed toward a gradual lower
ing of rigidity.
The wholesaler's inspection is generally stiffer than that of the manu
facturer. Diversity of rules is a sadly demoralizing element in lumber
circles.
Lumber sawn for special purposes {e. g., wagon bolsters) must be in
spected with a view to its adaptability for such special purpose.
A. Hardwood. The grade of a board depends on
1. Its width and length;
2. Its standard defects ;
3. The percentage of clear stock contained therein ;
4. The number of cuttings yielding such clear stock.
The following table shows average specifications prevailing for the
various grades of hardwood lumber in the U. S. markets.
The defects specified invariably indicate the coarsest stock admissible
in a given grade.
68
Forest Mensuration
Hardwood
Lumber Specifications.
Designation
Minimum
Actual
Allows of
of
Grade.
Len'h
feet.
Wi'th
inch
es.
Length
feet.
Width
inches.
No. of
standard
defects.
Rate
of clear
stock.
Con'd in
c't'ngsnot
more than
Firsts
Seconds
IO
8
IO
8
8
6
i o & over
i o & over
8
8
i o & over
io & over
i o & over
io & over
8&9
io & over
8&9
io & over
6& 7
8&9
IO & II
1 2 & over
none
one
none
one
none
one
two
three
"3
a
u
V
a
o
o
In
Ph
No. i Com...
6
8
6
4
6
6
8
8
8& io
12 to 1 6
6 to 8
9 & over
4
5
6 & over
6 & over
none
one
none
one
all
all
all
all
§
I
I
I
I
2
3
No. 2 Com.. .
6
3
6 to io
12 to 1 6
i
3
4
No. 3 Com.. .
4
3
\
B. Softwoods. Softwood lumber is inspected from its best side
Under "edgegrain" is understood lumber the face of which forms an* angle
of less than 45 degrees with the plain of the medullary rays contained in
the board. All other lumber is termed "flat grain" or "slash grain," also
"bastard grain."
I. Finishi?ig Lumber, 1" to 2" thick, dressed one or two sides.
1. First and second clear,
up to 8" wide ; absolutely clear ;
10" wide; one small defect permitted;
12" and over wide; \ of stock may have one standard knot or
its equivalent.
2. Third clear,
allows of twice as many defects.
II. Flooring, 1" thick and 3" or 4" or 6" wide before dressing; either
with hollow back or with solid back ;
1. A, B and C flat grain flooring ; wherein "A" is clear and "B" al
lows of one or two standard defects ;
2. A, B and C edgegrain flooring ; with the same allowance ;
3. No. 1 and No. 2 fence flooring.
Forest Mensuration 69
III. Ceiling, f, $ and  inch thick; 3, or 4, or 6 inches wide.
1. "A" ceiling and "B" ceiling, with small defects only;
2. No. 1 and No. 2 common ceiling, with one and two standard de
fects, or their equivalent.
IV. Drop Siding, which is either "shiplapped" or "tongued and grooved;"
it is %" thick and 3^ or 5J inches wide. Grades A, B and No. 1
common.
V. Bevel Siding, which scales T y at the thin edge and \" at the thick
edge, resawn from stock dressed to £$" x 5$". Grades as under IV.
VI. Partition, measuring f " x 3J" or " x 5I". Grades as under IV.
VII. Common Boards, graded as No. 1, No. 2 and No. 3 common boards,
8", 10" or 12" wide, dressed one or two sides, or rough.
VIII. Fencing, graded as No. 1, No. 2 and No. 3 fencing, 3", 4" or 6" wide.
The grade "No. 3" includes defective lumber with knotholes, red
rot, very wormy patches, etc., on \ of the length of the board.
Fencing is either dressed or rough.
CHAPTER V.— STUMPAGE VALUES
PARAGRAPH CII.
STUMPAGE VALUES.
Forestry is a business ; the forest largely represents its business invest
ment ; its purpose is the raising of money, of dividends.
Thus it is with investments and the dividends therefrom that the fores
ter is concerned; and it is the task of "forest finance" and "forest manage
ment" to ascertain the factors and to regulate the components of such
investments.
Forest mensuration, as a subsidiary to forest management, may well
devote a chapter to the measurement of the stumpage value of trees.
Stumpage value is the price which a tree brings or should bring if it
were sold on the stump.
The stumpagevalue of a tree depends on the value of the lumber con
tained therein and obtained therefrom, deducting the total expense of
lumber production (logging, milling, shipping, incidentals.)
Since the value of lumber fluctuates, as well as the cost of production,
stumpage values are subject to continuous variation. The tendency of
stumpage prices, all over the world, is a tendency to rise — especially so
in countries of rapid development, rapid increase of population and in
adequate provisions for regrowth.
70 Forest Mensuration
The cost of production is composed about as follows :
i. Expense of logging and log transportation, varying locally be
tween $2 and $5 per i,ooo' b. m.
2. Expense of milling, varying between $1.50 and $5 per 1,000' b. m.
3. Expense of freightage of lumber to the consuming market,
amounting per 1,000' b. m. to $1.50 for very short hauls; to
$12 for a haul from Atlanta to Boston; to $21 for a haul across
the continent from Portland (Oregon) to New England.
Freight rates have, in the long run, a decided downward tendency.
Still, with a majority of the lumber produced in the U. S., the item
"freight" forms the chief expense of production.
For Pisgah Forest a reduction of freight rates equalling 1 cent per 100
lbs. involves a net gain for the owner of approximately $60,000. In this
possibility lies one of the strongest arguments for conservative lumbering.
An increase of the price of lumber from $20 to $21 at the place of con
sumption endears the lumber to the consumer by 5% ; the owner of the
forest now valuing his stumpage at $5 will eventually experience this in
crease as a 20% increase of stumpage values.
The only factors of stumpagevalues, which the owner himself — unaided
by the development of the country — may influence, consist in the expense
of logging and log freighting, and in the expense of milling, the former
largely depending on the quality of available means of transportation, the
latter governed by the quality of the sawmill.
In ascertaining the stumpagevalue of a tree the forester considers :
a. The cost per 1,000' b. m. of logging it, of milling it and of freight
ing its timber;
b. The volume of timber contained in the tree, by grades ;
c. The value of such lumber, by grades.
If a tree contains
45% of lumber worth $31 per 1,000' b. m.
It is necessary to find Stoetzer's constant factor of increment or to
ascertain the relative increment of the sectional areas of the sample trees
at 0.45 of their heights.
35% of lumber worth $21 per 1,000' b. m.
15% of lumber worth $16 per 1,000' b. m.
5% of lumber worth $8 per 1,000' b. m.
then, the lumber value of the tree, per 1,000' b. m., is
45 x 31 + 35 x 21 + 15 x if, + 5 x 8
100
= $24.10
Deducting from this figure the expense of logging, milling and freight
ing, the actual stumpagevalue, per 1,000' b. m., is derived.
The actual prices paid for stumpage in the U. S. fall deeply below the
figures which a testcalculation is apt to yield.
Forest Mensuration
71
This discrepancy may be explained, above all, by
Ignorance of owners of stumpage ;
Agents' and dealers' profits ;
Incidental expenses overlooked.
Stumpagevalues show a rapid decrease with the increase of the dis
tance separating the tree from the nearest railroad or stream.
The grades of lumber and their proportion obtainable from logs of
given species, diameter and soundness (including presence and location
of defects) can be ascertained only by testsawing in the mill.
This has been done in 1896 for yellow poplar at Biltmore (bandsaw
mill). The stumpagevalues then ascertained are shown by the follow
ing table :
Market Value of Poplar Stumpage in Western North Carolina, Per
Tree, in Cents.
<*!
Under good
Jnder average
Under poor
O
4>
conditions.
conditions.
conditions.
be
Logging and Milling
Logging and Milling
Logging and Milling
<u b
. ui
expenses being per
■ t/j
expenses being per
• in
expenses being per
5 &
H_=
n
1000 feet B. M.
Eg
1000 feet B. M.
.So
1000 feet B. M.
<
SS
$9
Sio
$n
O.S
$9
$10 $11
P.S
$9 Sio
$11
IOo
Nega
Nega
Nega
Nega
Nega Nega
Nega Nega
Nega
tive.
tive.
tive.
tive.
tive.
tive.
tive.
tive.
tive.
I20
18.8
8
«
«.
«
<<
«
«
■ <
«
140
21 .3
40
25
"
18
2
4
"
"
"
"
"
160
235
105
7 2
2
20
4
22
5
"
"
"
"
i So
257
265
170
98
2 2
4
67
35
"
"
"
"
200
27.7
445
325
23O
24
3
160
103
3D
18
5
"
"
"
220
29.6
620
465
350
2h
287
200
109
20
O
7
"
"
240
27
5
430
330
210
21
3
27
3
"
260
460
330
22
1
60
25
"
280
45
"
300
5
320
30
Footnote : Dots below a column of figures indicate higher values, not
specifically ascertained.
The values above the columns of figures are all negative and were not
ascertained specifically either.
It is to be hoped that similar tests will be made for our leading species
on a large scale by the U. S. Forest Service or by the various associations
of lumber manufacturers. Conservative forestry as a business badly re
quires data allowing to estimate the actual value of logs, and hence of
trees, if the uncertainty of financial results now checking the progress of
conservative forestry in America is to be definitely reduced.
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